ConferenceTimetableSummary - Staging site · 3:10pm Marty Ross: How I teach, why the Mathologer is evil, and other indiscrete thoughts In this shamelessly narcissistic talk I will

Conference Timetable Summary

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Lunch

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WIMSIGDinner

Campus Centre

RegistrationSouth 1

Opening Ceremony

Lectures byPrize Winners

South 1

Plenary talkKriegerSouth 1

Plenary talkSikora

SpecialSessions

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EducationAfternoon

EducationAfternoon

WelcomeReception

Cinque Lire Cafe

Plenary talkJoshi

Plenary talkan Huef

Debate

Special Sessions

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Plenary talkUlcigrai

Plenary talkSteinberg

Plenary talkTrudgian

Special Sessions

Plenary talkRylands

AustMS AGM

Conference Dinner

MCG

Plenary talkGiga

Plenary talkNorbury

Plenary talkSamotij

Special Sessions

Special Sessions

1

ContentsForeword 4

Conference Sponsors 5

Conference Program 6

Education Afternoon 7

Session 1: Plenary Lectures 8

Special Sessions2. Algebra 93. Applied and Industrial Mathematics 104. Category Theory 115. Combinatorics and Graph Theory 126. Computational Mathematics 147. Dynamical Systems and Ergodic Theory 158. Financial mathematics 169. Functional Analysis, Operator Algebra, Non-commutative Geometry 17

10. Geometric Analysis and Partial Differential Equations 1811. Geometry including Differential Geometry 2012. Harmonic and Semiclassical Analysis 2113. Inclusivity, diversity, and equity in mathematics 2214. Mathematical Biology 2315. Mathematics Education 2416. Mathematical Physics, Statistical Mechanics and Integrable systems 2517. Number Theory and Algebraic Geometry 2718. Optimisation 2819. Probability Theory and Stochastic Processes 3020. Representation Theory 3221. Topology 33

Conference Timetable 1Tue 3 December 2019 35Wed 4 December 2019 39Thu 5 December 2019 47Fri 6 December 2019 50

List of Registrants 54

Plenary Abstracts 61

Special Session Abstracts 612. Algebra 653. Applied and Industrial Mathematics 694. Category Theory 715. Combinatorics and Graph Theory 736. Computational Mathematics 797. Dynamical Systems and Ergodic Theory 838. Financial mathematics 869. Functional Analysis, Operator Algebra, Non-commutative Geometry 89

10. Geometric Analysis and Partial Differential Equations 9111. Geometry including Differential Geometry 9512. Harmonic and Semiclassical Analysis 9813. Inclusivity, diversity, and equity in mathematics 10014. Mathematical Biology 10315. Mathematics Education 107

16. Mathematical Physics, Statistical Mechanics and Integrable systems 11017. Number Theory and Algebraic Geometry 11518. Optimisation 11819. Probability Theory and Stochastic Processes 12220. Representation Theory 12721. Topology 129

Index of Speakers 133

3

Foreword

Welcome to Monash University’s Clayton Campus for the 63rd Annual Meeting of the Australian Mathe-matical Society. It is very exciting to see so many academics and graduate students coming together fromaround Australia and 26 other countries to exchange ideas and to celebrate mathematics.This year we have a few innovations, including plenary lectures focussing on education and on equity anddiversity. We also, for the first time, have a special session on Inclusivity, diversity, and equity in mathemat-ics. Another innovation this year is bush dancing at the conference dinner on Thursday night – make sureyou wear your dancing shoes!An event of this scale does not happen without a lot of people pitching in. I would particularly like to thankall the people listed below for all their assistance in making this event happen.Finally, I wish you a productive and enjoyable week at Monash,

Prof Ian Wanless

Conference Director

Program Committee

Ben Burton (UQ)Alan Carey (ANU)Michael Coons (Newcastle)Alice Devillers (UWA)Vlad Ejov (Flinders)Roozbeh Hazrat (WSU)Birgit Loch (Latrobe)Giang Nguyen (Adelaide)Milena Radnovic (Sydney)Vera Roshchina (UNSW)Ian Wanless (Monash)Valentina Wheeler (Wollongong)

Local Organising Committee

Julie Clutterbuck – Special sessionsGregoire Loeper – TreasurerAngelika Nikolov-Arvela – SecretaryJessica Purcell – WIMSIG dinnerDaniel Mathews – ChildcareDaniel Horsley – DebateMark Flegg – This documentDeborah Jackson – NametagsJohn Chan, Jerome Droniou, Jeremy Hague – WebsiteJohn Banks – Registration systemGertrude NayakAnna HaleyGreg Markowsky

4

Conference Sponsors

Special thanks also to Prof Kate Smith-Miles through the Georgina Sweet Award component of herARC Australian Laureate Fellowship, for sponsoring the Women in Mathematics dinner.

5

Conference Program

Overview of the Academic Program

There are 305 talks, including 11 plenary lectures and 20 special sessions. The Education Afternoon onTuesday comprises talks of interest to all mathematical educators.

B Conference Timetable – page 1

Tue 3 December 2019 – page 35Wed 4 December 2019 – page 39Thu 5 December 2019 – page 47Fri 6 December 2019 – page 50

Plenary Lecturers

Yoshikazu Giga (University of Tokyo)Astrid an Huef (Victoria University of Wellington) – Hanna Neumann LecturerNalini Joshi (University of Sydney) – ANZIAM LecturerHolly Krieger (Cambridge) – Mahler LecturerPaul Norbury (University of Melbourne)Leanne Rylands (Western Sydney University)Wojciech Samotij (Tel Aviv University) – ECR LecturerJoanna Sikora (ANU)Benjamin Steinberg (City University of New York)Tim Trudgian (UNSW Canberra)Corinna Ulcigrai (University of Zurich)B Timetable of Plenary Lectures – page 8

Special Sessions

1. Plenary – page 622. Algebra – page 653. Applied and Industrial Mathematics – page 694. Category Theory – page 715. Combinatorics and Graph Theory – page 736. Computational Mathematics – page 797. Dynamical Systems and Ergodic Theory – page 838. Financial mathematics – page 869. Functional Analysis, Operator Algebra, Non-commutative Geometry – page 89

10. Geometric Analysis and Partial Differential Equations – page 9111. Geometry including Differential Geometry – page 9512. Harmonic and Semiclassical Analysis – page 9813. Inclusivity, diversity, and equity in mathematics – page 10014. Mathematical Biology – page 10315. Mathematics Education – page 10716. Mathematical Physics, Statistical Mechanics and Integrable systems – page 11017. Number Theory and Algebraic Geometry – page 11518. Optimisation – page 11819. Probability Theory and Stochastic Processes – page 12220. Representation Theory – page 12721. Topology – page 129

6

Conference Program

Education Afternoon (Tues in G03)

2:20pm Julia Collins and Katherine Seaton: Knitting and Folding MathematicsMathematical thinking is not confined to mathematicians, but one place you may not expect tofind it is in the world of crafts. Even the most maths-anxious knitters will display an astonish-ing familiarity with concepts from geometry, topology, number theory and coding, while modernorigami artists are turning to mathematical algorithms to create models previously thought to beunfoldable. This talk will highlight a number of surprising connections between maths and craft,and will be followed by a hands-on session facilitated by Maths Craft Australia where people cancreate some mathematical craft for themselves. (Knitting/crochet needles and origami paper willbe provided, but participants are also encouraged to bring their own! Knitting in the audience isstrictly encouraged.)

3:10pm Marty Ross: How I teach, why the Mathologer is evil, and other indiscrete thoughtsIn this shamelessly narcissistic talk I will reveal the One True Secret to teaching mathematics.Along the way I will explain why you can and should ignore STEM, calculators, Mathematica, iPads,the evil Mathologer, constructivism, growth mindset, SOLO, Bloom, flipping classrooms, centeringchildren, lesson plans, skeleton notes, professional standards and professional development andmany other modern absurdities.

3:35pm David Treeby: How to Instil Mathematical Culture in Secondary EducationOver the past few decades, mathematicians have ceded the educational space to two groups:mathematics educators and technology companies. This has had a dire effect on what mathemat-ics is taught and how it is taught. The result is a commodified brand of distorted mathematics. Thistalk will focus on how some well-resourced schools have resisted these changes, and how broadand equitable change will require the support of working mathematicians and their professionalbodies.

4pm Burkard Polster – Mathologer: explaining tricky maths on YouTubeIn this session I’ll talk about my experience running the YouTube channel Mathologer and I’ll giveyou a sneak peek of the video that I am currently working on.

Social ProgramÏ 6:15pm for 6:45pm Mon

WIMSIG DinnerCampus Centre

Ï 6pm TuesWelcome receptionCinque Lire Cafe

Ï 6:30pm ThursConference BanquetOlympic Room, Melbourne Cricket Ground (MCG)

Annual General Meeting of the SocietyÏ 4pm Thurs

AustMS AGMLecture Theatre G81 (Same venue as most plenaries)

Conference Information Desk

The registration/information desk will be located outside the venue for the plenary talks (South 1 on TueMorning, and G81 for the rest of the week). This desk will be staffed before the opening ceremony and eachday during morning tea. If you have any issues you can also email [email protected]

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Plenary Lectures in South 1 [Krieger] or G81 [Others]

B Tue 3 December 2019

11:00 Ï Holly Krieger (University of Cambridge)

Unlikely intersections in arithmetic and dynamics

13:30 Ï Joanna Sikora (Australian National University)

Advancing women in Australian Mathematics: context, challenges and achievements

B Wed 4 December 2019

09:00 Ï Nalini Joshi (The University of Sydney)

When applied mathematics collided with algebra

10:30 Ï Astrid an Huef (Victoria University of Wellington)

Algebraic systems of isometries

B Thu 5 December 2019

09:00 Ï Corinna Ulcigrai (University of Zurich)

Shearing and mixing in surface flows

10:30 Ï Benjamin Steinberg (City University of New York)

Monoids in Representation Theory, Markov Chains, Combinatorics and Operator Algebras

11:30 Ï Timothy Trudgian (UNSW Canberra)

Primes = Hard +O(1)

15:10 Ï Leanne Rylands (Western Sydney University)

The mathematics problem

B Fri 6 December 2019

09:00 Ï Yoshikazu Giga (University of Tokyo)

On total variation flow type equations

10:30 Ï Paul Norbury (The University of Melbourne)

Enumerative geometry via the moduli space of super Riemann surfaces.

11:30 Ï Wojciech Samotij (Tel Aviv University)

Large deviations in random graphs

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Special Session 1: Algebra

Organisers Heiko Dietrich, Anne Thomas

Contributed TalksB Wed 4 December 2019

13:30 Jeroen Schillewaert (University of Auckland)On exceptional Lie geometries (p. 68)

13:55 Subhrajyoti Saha (Monash University)Skeleton groups and their isomorphism problem (p. 67)

14:20 Primoz Moravec (University of Ljubljana)Gaps in probabilities of satisfying some commutator identities (p. 66)

14:45 Michal Ferov (The University of Newcastle)Separating conjugacy classes in wreath products of groups (p. 65)

15:35 Marcos Origlia (Monash University)Simply transitive NIL-affine actions of solvable Lie groups (p. 67)

16:00 Santiago Barrera Acevedo (Monash University)Cocyclic Hadamard matrices of order 4p (p. 65)

16:25 James Mathew Koussas (La Trobe University)Varieties of semiassociative relation algebras (p. 66)

16:50 Lauren Thornton (University of the Sunshine Coast)On properties of descending chains (p. 68)

17:15 Alejandra Garrido (The University of Newcastle)Locally compact topological full groups are locally finite (p. 65)

17:40 Colin David Reid (The University of Newcastle)Locally compact piecewise full groups of homeomorphisms of the Cantor set (p. 67)


13:30 Amnon Neeman (Australian National University)Non Fourier-Mukai functors (p. 67)

13:55 Robert McDougall (University of the Sunshine Coast)Interpreting a radical theory identity for classes of associative rings (p. 66)

14:20 Abdullahi Umar (Khalifa University of Science, Technology)Some Remarks on monoids of contraction mappings of a finite chain (p. 68)


13:30 James East (Western Sydney University)Presentations for diagram algebras and categories (p. 65)

13:55 Richard Garner (Macquarie University)Generalising the étale groupoid–complete pseudogroup correspondence (p. 65)

14:20 Tim Stokes (University of Waikato)Demonic composition and inverse semigroups. (p. 68)

15:10 Tomasz Kowalski (La Trobe University)A little beyond wreath and block (p. 66)

15:35 Thomas Quella (The University of Melbourne)Takiff superalgebras and conformal field theory (p. 67)

16:00 Marcel Jackson (La Trobe University)Algebras defined by equations (p. 66)

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Special Session 2: Applied and Industrial Mathematics

Organisers Christian Thomas, Lele (Joyce) Zhang

Keynote TalksB Tue 3 December 2019

15:10 Terry O’Kane (CSIRO)Simple Markovian closures for inhomogeneous turbulence (p. 69)

Contributed TalksB Tue 3 December 2019

14:20 Dylan Harries (CSIRO)Applications of temporally regularised matrix factorisations to the analysis of climate data(p. 69)

16:00 Samithree Rajapaksha (Monash University)Approximating Link Travel Time Distributions (p. 70)

16:25 Vassili Kitsios (CSIRO)Ensemble transform Kalman filter estimation of thermodynamic parameters in a coupledgeneral circulation model (p. 69)

16:50 Sevvandi Priyanvada Kandanaarachchi (Monash University)DOBIN: dimension reduction for outlier detection (p. 69)

17:15 Lele (Joyce) Zhang (The University of Melbourne)Courier route optimization with unloading bays information and reservation systems (p. 70)

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Special Session 3: Category Theory

Organisers David Roberts, Marcy Robertson

Keynote TalksB Wed 4 December 2019

13:30 Richard Garner (Macquarie University)The free tangent category on an affine connection (p. 71)


14:20 Michelle Strumila (The University of Melbourne)Graphical Sets and Mapping Class Groups (p. 72)

14:45 Giacomo Tendas (Macquarie University)Regular Theories Enriched Over Finitary Varieties (p. 72)

15:35 Martina Rovelli (The Australian National University)An embedding of the homotopy theory of 2-categories into that of 2-complicial sets (p. 71)

16:00 Bryce Clarke (Macquarie University)Characterising split opfibrations using lenses (p. 71)

16:25 Bregje Pauwels (The University of Sydney)t-structures and approximable triangulated categories (p. 71)

16:50 David Roberts (The University of Adelaide)Localising by spans and cospans, and functoriality of associated algebras (p. 71)

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Special Session 4: Combinatorics and Graph Theory

Organisers Joanne Hall, David Wood


15:10 Andrii Arman (Monash University)Generation of random graphs with given degrees (p. 73)


14:20 Benjamin Jones (Monash University)Excluded minors for classes of binary functions (p. 76)

16:00 Rui Zhang (Monash University)Bounded Difference Inequalities for Graph-Dependent Random Variables (p. 78)

16:25 Matthias Fresacher (University of Adelaide)Learning Large Random Graphs Via Group Queries (p. 75)

16:50 Angus Southwell (Monash University)Counting automorphisms of random trees with martingales (p. 77)

17:15 Richard Brak (The University of Melbourne)Universal Bijections for Positive Algebraic Structures (p. 73)

17:40 Kevin Limanta (University of New South Wales)A curious bijection between Dyck paths (p. 76)


13:30 Nicholas Cavenagh (University of Waikato)Heffter Arrays with compatible and simple orderings (p. 73)

13:55 Ajani De Vas Gunasekara (Monash University)On determining when small embeddings of partial Steiner triple systems exist (p. 74)

14:20 Adam Gowty (Monash University)New bounds on the maximum size of Sperner partition systems (p. 75)

14:45 Daniel Horsley (Monash University)Generating digraphs with derangements (p. 76)

15:35 Guillermo Pineda-Villavicencio (Deakin University)Minkowski decompositions of polytopes via geometric graphs (p. 77)

16:00 Michael Payne (La Trobe University)Geometric hypergraph colouring problems (p. 77)

16:25 Adam Mammoliti (Monash University)On the Cyclic Matching sequenceablility of regular graphs (p. 76)

16:50 Michael James Gill (Monash University)Perfect 1-factorisations of K16 (p. 75)

17:15 William Crawford (Monash University)Properties of the polytope of polystochastic matrices (p. 74)

17:40 Graham Farr (Monash University)Some problems suggested by the Online Graph Atlas project (p. 74)

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4. Combinatorics and Graph Theory


13:30 Amin Sakzad (Monash University)Middle Product Learning With Errors (p. 77)

13:55 Lynn Batten (Deakin University)How generic ring algorithms and labelled binary trees helped solve an outstanding factoringproblem in number theory. (p. 73)

14:20 Andrea Burgess (University of New Brunswick)The firebreak problem (p. 73)


13:30 Sanming Zhou (The University of Melbourne)The vertex-isoperimetric number of the incidence graphs of unitals and finite projectivespaces (p. 78)

13:55 Greg Markowsky (Monash University)The Cheeger constant for distance-regular graphs. (p. 77)

14:20 Binzhou Xia (The University of Melbourne)Some examples of nonnormal Cayley graphs on nonabelian simple groups (p. 78)

15:10 Joanne Hall (Royal Melbourne Institute of Technology)Constructions of Difference Covering Arrays using Skolem sequences (p. 75)

15:35 Vesa Kaarnioja (University of New South Wales)An improved lower bound on Hong and Loewy’s numbers (p. 76)

16:00 Son Hoang Dau (RMIT University)MaxMinSum Steiner Systems for Access-Balancing in Distributed Storage (p. 74)

16:25 Kevin Hendrey (Institute for Basic Science)Covering radius in the Hamming permutation space (p. 75)

13

Special Session 5: Computational Mathematics

Organisers Bishnu Lamichhane, Quoc Thong Le Gia


13:55 Gianmarco Manzini (Consiglio Nazionale delle Ricerche (CNR) - Italy)The Virtual Element Method for solving partial differential equations on unstructuredpolytopal meshes (p. 81)


13:30 Markus Hegland (Australian National University)Approximating functions of the precision matrix of Gaussian processes (p. 80)

14:45 Hailong Guo (The University of Melbourne)Unfitted Nitsche’s method for computing edge modes in photonic graphene (p. 80)

15:35 Oliver krzysik (Monash University)Parallel time integration of hyperbolic PDEs (p. 80)

16:00 Michael Clarke (UNSW Sydney)Uncertainty Quantification for the Linear Elastic equations (p. 79)

16:25 El Houssaine QUENJEL (Nice Sophia Antipolis University)A stable finite volume scheme for nonlinear diffusion equations on general 2D meshes (p.81)

16:50 Riya Aggarwal (The University of Newcastle)Bragg Edge Neutron Transmission Strain Tomography using the Finite Element Method (p.79)

17:15 Mark Joseph McGuinness (Victoria University of Wellington)Pressure Buildup in Surtseyan Ejecta (p. 81)

17:40 Janosch Rieger (Monash University)An approach to electrical impedance tomography in unknown domains (p. 81)

18:05 Martin Helmer (Australian National University)Probabilistic Saturations and Alt’s Problem in Mechanism Design (p. 80)


13:30 Thanh Tran (University of New South Wales)A posteriori error estimation for nonlinear elliptic equations (p. 82)

13:55 Jerome Droniou (Monash University)High-order numerical schemes for degenerate elliptic equations (p. 79)

14:20 Quoc Thong Le Gia (University of New South Wales)A multiscale radial basis function method for severely ill-posed problems on spheres (p. 80)

14

Special Session 6: Dynamical Systems and ErgodicTheory

Organisers Jason Atnip, Andy Hammerlindl


13:30 Anoop Sivasankaran (Khalifa University of Science, Technology)An empirical stability analysis of restricted Four-Body model (p. 85)

13:55 Divahar Jayaraman (The University of Adelaide)Multiscale modelling enables prediction and simulation of floods and tsunamis (p. 84)

14:20 Courtney Rose Quinn (CSIRO)Application of local attractor dimension to reduced space strongly coupled data assimilationfor chaotic multiscale systems (p. 84)

14:45 Sam Jelbart (The University of Sydney)Blowing-up essential singularities in singularly perturbed problems (p. 84)

16:00 Lachlan Smith (The University of Sydney)Model reduction for the collective dynamics of networks of coupled oscillators (p. 85)

16:25 Gary Froyland (University of New South Wales)A spectral approach for quenched limit theorems for random dynamical systems (p. 83)

16:50 Jason Atnip (University of New South Wales)Conformal and Invariant Measures for Random Covering Weighted Systems (p. 83)

17:15 Fawwaz Batayneh (University of Queensland)On the number of ergodic absolutely continuous invariant measures for higher dimensionalrandom dynamical systems (p. 83)

17:40 Cecilia Gonzalez-Tokman (The University of Queensland)Characterization and perturbations of the Lyapunov spectrum of a class of Perron-Frobeniusoperator cocycles (p. 83)


13:30 Kenneth James Palmer (National Taiwan University)On Sil’nikov saddle-focus homoclinic orbits (p. 84)

13:55 Davide Ravotti (Monash University)A geometric proof of Ratner’s mixing rates for the horocycle flow (p. 85)

14:20 Sean Gasiorek (The University of Sydney)On the Dynamics of Inverse Magnetic Billiards (p. 83)

15

Special Session 7: Financial mathematics

Organisers Ivan Guo, Zhou Zhou


15:35 Jan Obloj (University of Oxford)Robust finance: data-driven approach to pricing, hedging and risk management (p. 87)


13:30 WEI Ning (Monash University)Portfolio optimization with a prescribed terminal wealth density by deep optimal transport(p. 86)

13:55 Ivan Guo (Monash University)Convex duality in robust hedging and optimal stopping problems (p. 86)

14:20 Kihun Nam (Monash University)Non-Markovian Multidimensional Quadratic BSDE (p. 86)

14:45 Kenneth James Palmer (National Taiwan University)Path Independence of Exotic Options and Convergence of Binomial Approximations (p. 87)

16:25 Shiyi Wang (Monash University)Calibration of Local-Stochastic Volatility models by Optimal Transport (p. 87)

16:50 James Yang (The University of Sydney)Multiscale Linear-Quadratic Stochastic Optimal Control (p. 87)

17:15 Edward Kim (The University of Sydney)Vulnerable American Contracts with Extraneous Risks and Market Frictions (p. 86)


13:30 Libo Li (University of New South Wales)Mean-field stable CIR process (p. 86)

13:55 Anna Aksamit (The University of Sydney)Modelling additional information: filtration enlarged via a marked random time (p. 86)

14:20 Zhou Zhou (The University of Sydney)On the Notions of Equilibria for Time-inconsistent Stopping Problems in Continuous Time(p. 87)

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Special Session 8: Functional Analysis, OperatorAlgebra, Non-commutative Geometry

Organisers Galina Levitina, Geetika Verma


15:10 Hai-Long Her (The Australian National University)Fredholm Property of Operators from 2D String Field Theory (p. 89)

15:35 David Leonard Brook (The University of Adelaide)Higher twisted K-theory (p. 89)

16:00 Shaymaa Shawkat Kadhim Al-shakarchi (University of New South Wales)Isomorphisms of AC (σ) spaces. (p. 89)


13:30 Hendra Gunawan (Bandung Institute of Technology)Some geometric constants for Morrey spaces (p. 89)

13:55 Roozbeh Hazrat (Western Sydney University)The talented monoid of a directed graph (p. 89)

14:20 Geetika Verma (University of South Australia)Inversion of operator pencils on Banach space using Jordan chains (p. 89)

17

Special Session 9: Geometric Analysis and PartialDifferential Equations

Organisers Ting-Ying Chang, Todd Oliynyk


14:20 Jesse Gell-Redman (AMSI/University of Melbourne)Global methods for semi-linear hyperbolic equations (p. 92)

15:10 Volker Schlue (The University of Melbourne)On the stability of expanding black hole spacetimes (p. 93)

15:35 Christopher P Rock (UNSW Sydney)Higher-order Cheeger and Buser inequalities, and a dynamics application (p. 93)

16:00 Yilin Ma (The University of Sydney)The Semilinear Calderon Problem on Complex Manifolds (p. 93)

16:25 Florica Corina Cirstea (The University of Sydney)Existence of sharp asymptotic profiles of singular solutions to an elliptic equation with asign-changing nonlinearity (p. 91)

16:50 Yuhan Wu (University of Wollongong)Short time existence for higher order curvature flows with and without boundary conditions(p. 94)

17:15 Nicholas Fewster-Young (University of South Australia)Existence Results for Nonlinear Fractional Differential Equations (p. 92)

17:40 Maria Farcaseanu (The University of Sydney)Singular quasilinear elliptic equations with gradient dependent nonlinearities (p. 92)


13:30 Serena Dipierro (The University of Western Australia)A free boundary problem driven by the biharmonic operator (p. 92)

13:55 Paul Bryan (Macquarie University)Hyperbolic 3-manifolds, embeddings and an invitation to the Cross Curvature Flow (p. 91)

14:20 Julie Clutterbuck (Monash University)The fundamental gap in a negatively curved domain (p. 91)

14:45 Wenhui Shi (Monash University)An epiperimetric inequality approach to the parabolic Signorini problem (p. 94)

15:35 Stephen Lynch (University of Tubingen)A fully nonlinear flow of three-convex hypersurfaces (p. 93)

16:00 Romina Melisa Arroyo (University of Queensland)The prescribed Ricci curvature problem for naturally reductive metrics on compact Liegroups: general theory (p. 91)

16:25 Artem Pulemotov (The University of Queensland)The prescribed Ricci curvature problem for naturally reductive metrics on compact Liegroups: examples (p. 93)

16:50 Valentina-Mira Wheeler (University of Wollongong)Counterexamples to graph preservation under mean curvature flow (p. 94)

17:15 Yong Wei (Australian National University)Horospherically convex geometry in hyperbolic space and geometric flows (p. 94)

18

9. Geometric Analysis and Partial Differential Equations


13:30 Enrico Valdinoci (The University of Western Australia)Nonlocal minimal graphs in the plane are generically sticky (p. 94)

13:55 Zihua Guo (Monash University)Ill-posedness of the Camassa-Holm and related equations in the critical space (p. 92)

14:20 Matthew Kevin Cooper (University of New England)Symmetric biharmonic maps (p. 91)

15:10 Kwok-Kun Kwong (University of Wollongong)Quantitative comparison theorems in geometry (p. 92)

15:35 Sevvandi Priyanvada Kandanaarachchi (Monash University)Singularities of Axially Symmetric Volume Preserving Mean Curvature Flow (p. 92)

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Special Session 10: Geometry including DifferentialGeometry

Organisers Ramiro Augusto Lafuente, Gerd Schmalz

Keynote TalksB Thu 5 December 2019

13:55 A. Rod Gover (The University of Auckland)Distinguished curves and integrability in Riemannian and conformal geometry (p. 95)


15:10 Artem Pulemotov (The University of Queensland)The prescribed Ricci curvature equation on (SU (2)×SU (2))/U (1)r (p. 96)

15:35 Romina Melisa Arroyo (University of Queensland)On the signature of the Ricci curvature on nilmanifolds (p. 95)

16:00 Parsa Kavkani (The University of Adelaide)Group Extensions and Bundle Gerbes (p. 95)

16:50 Gerd Schmalz (University of New England)Kähler manifolds, Sasakian manifolds and generalised Taub-NUT solutions (p. 96)

17:15 Jeremy Nugent (University of New South Wales)Superintegrable systems (p. 96)


13:30 Benjamin Blake McMillan (The University of Adelaide)Conservation laws and parabolic Monge-Ampere equations (p. 95)


13:30 Yuri Nikolayevsky (La Trobe University)On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space (p. 96)

13:55 Andreas Vollmer (University of New South Wales)Second order superintegrable systems in arbitrary dimension (p. 97)

14:20 Krzysztof Krakowski (Cardinal Stefan Wyszynski University in Warsaw)Rolling Symmetric Spaces (p. 95)

15:10 Marcos Origlia (Monash University)Locally conformal Käler or symplectic structures on compact solvmanifolds (p. 96)

15:35 Owen Dearricott (The University of Melbourne)Positive curvature in dimension seven (p. 95)

20

Special Session 11: Harmonic and SemiclassicalAnalysis

Organisers Zihua Guo


13:30 Xuan Duong (Macquarie University)Sharp endpoint estimates for Schrödinger groups (p. 98)

13:55 Andrew Hassell (Australian National University)A Fredholm approach to solving semilinear evolution equations (p. 98)

14:20 Alex Amenta (University of Bonn)Vector-valued time-frequency analysis and the bilinear Hilbert transform (p. 98)

14:45 Volker Schlue (The University of Melbourne)Scattering from infinity for semi-linear wave equations with weak null condition (p. 99)

15:35 Hamed Baghal Ghaffari (The University of Newcastle)Construction of Multidimensional Prolate Spheroidal Wave Functions (p. 98)

16:00 Trang Thi Thien Nguyen (University of South Australia)Non-homogeneous T (1) theorem for singular integrals on product quasimetric spaces (p.99)

16:25 Guillermo Javier Flores (Universidad Nacional de Cordoba)Weighted Lebesgue and BMO norm inequalities for the Calderon and Hilbert operators (p.98)

16:50 Fu Ken Ly (The University of Sydney)An improved heat kernel bound for certain magnetic Schrodinger operators. (p. 99)


13:30 Lesley Ward (University of South Australia)Product Hardy space theory on spaces of homogeneous type via orthonormal wavelet bases(p. 99)

13:55 Adam Sikora (Macquarie University)Spectral multipliers without semigroup framework and application to random walks (p. 99)

14:20 Ji Li (Macquarie University)Commutators of Cauchy-Szego type integrals for domains in C n with minimal smoothness(p. 98)

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Special Session 12: Inclusivity, diversity, and equity inmathematics

Organisers Amie Albrecht


15:10 Nalini Joshi (The University of Sydney)A call to action (p. 101)

15:35 Benjamin Burton (University of Queensland)Diversity at the Olympiads: Culture change in elite competition (p. 100)

16:00 Rowena Ball (The Australian National University)Maths on country (p. 100)

16:25 Yudhistira Andersen Bunjamin (UNSW Sydney)Equity considerations and design of mathematics outreach to schools (p. 100)

16:50 Julia Collins (Edith Cowan University)CHOOSEMATHS: approaches to increasing female participation in advanced schoolmathematics (p. 100)

17:15 Valentina-Mira Wheeler (University of Wollongong)Women in mathematics: one perspective on things that work so far and things that could bedone in the future (p. 102)


13:30 Jessica Purcell (Monash University)WIMSIG resources and initiatives to support careers (p. 102)

13:55 Daniel Mathews (Monash University)Childcare at a large mathematical conference (p. 101)

14:20 Matthew Mack (Multiple Universities)Improving accessibility in mathematics (p. 101)

14:45 Jacqui Ramagge (The University of Sydney)Hiring for diversity (p. 102)

15:35 Heather Lonsdale (Curtin University)Creating a critical mass of females in engineering mathematics classrooms (p. 101)

16:00 Collin Grant Phillips (The University of Sydney)Responsive Techniques for Teaching Australian, Indigenous School Students: What PartDoes Culture Play in Teaching Mathematics? (p. 102)

16:25 Asha Rao (Royal Melbourne Institute of Technology)Nurture, gender differences and spatial abilities (p. 102)

16:50 Marcy Robertson (The University of Melbourne)Improving the process of organizing conferences and special semesters (p. 102)

17:15 John Ormerod (The University of Sydney)Descartes was wrong - The psychology of safety and its implications to equality, diversity,and inclusion (p. 101)

22

Special Session 13: Mathematical Biology

Organisers Pascal R Buenzli, Federico Frascoli


13:30 Michael Stumpf (The University of Melbourne)The origins of heavy-tailed laws in biology (p. 105)


14:20 timothy hewson (University of Tasmania)Graded rings of Markov invariants (p. 103)

14:45 Julia Shore (University of Tasmania)The ancient Operational Code is embedded in the amino acid substitution matrix and aaRSphylogenies (p. 105)

15:35 Venta Terauds (University of Tasmania)Symmetry and redundancy: choosing the right algebra for circular genome distancecomputations (p. 105)

16:00 Jeremy Sumner (University of Tasmania)The Markov embedding problem from an algebraic perspective (p. 105)

16:25 Chad Mathew Clark (Western Sydney University)An Algebraic Inversion-Deletion Model for Bacterial Genome Rearrangement (p. 103)

16:50 Joshua Stevenson (University of Tasmania)Investigating rank-based approaches for inferring phylogenies (p. 105)

17:15 Adarsh Kumbhari (The University of Sydney)Emergent signal processing in T cells via regulatory immune mechanisms (p. 104)

17:40 Pantea Pooladvand (The University of Sydney)Modelling the Immune Response of CD4+ T cells: An intimate relationship between T cellsand APCs (p. 104)


13:30 Sukhen Das (Jadavpur University)Study of HIV in-host model through multi-pathways infection under different blockers :local and global analysis (p. 103)

13:55 Nandadulal Nandadulal Bairagi (Jadavpur University)Pattern formation in a reaction-diffusion predator-prey-parasite model with prey infectionunder the influence of ecological and epidemiological parameters (p. 104)

14:20 Dipak Kumar Kesh (Jadavpur University)Role of induced plant volatile and refuge in tritrophic model (p. 104)


13:30 Andrew Francis (Western Sydney University)The space of tree-based phylogenetic networks (p. 103)

13:55 Lucy Ham (The University of Melbourne)Extrinsic noise and heavy-tailed distributions in gene expression (p. 103)

23

Special Session 14: Mathematics Education

Organisers Deborah King


13:30 Poh Hillock (The University of Queensland)Blended learning in a large first year mathematics course (p. 107)

13:55 Simon James (Deakin University)Peer assessment and feedback - in class and online (p. 108)

14:20 Jennifer Palisse (The University of Melbourne)Can Comparative Judgement Improve Student Performance with Rational Inequalities? (p.108)

14:45 Joshua Capel (UNSW Sydney)Learning and Teaching in a Digital world (p. 107)

16:00 Jelena Schmalz (University of New England)Mathematics Enrichment Program at UNE – from Primary School to University (p. 109)

16:25 Renu Choudhary (Auckland University of Technology)Empowering, Engaging and Enhancing Students’ Learning using a Pen-Enabled Tablet (p.107)

16:50 Diane Donovan (The University of Queensland)Should I apply for a Teaching Award (p. 107)


13:30 Jennifer Palisse (The University of Melbourne)Making the Grade: Do Mathematics Marks Matter to Women in STEM (p. 108)

13:55 Jonathan Kress (University of New South Wales)Assessment in First Year Mathematics (p. 108)

14:20 Donald Shearman (Western Sydney University)Does the Effectiveness of Mathematics and Statistics Support Depend on Students’Mathematical Background? (p. 109)

15:10 Deborah Jackson (La Trobe University)Igniting interest, inspiration, investigation and intrigue within mathematics support. (p. 107)

15:35 Terence Mills (La Trobe University)Can Kuhn revolutionise mathematics teaching? (p. 108)

24

Special Session 15: Mathematical Physics, StatisticalMechanics and Integrable systems

Organisers Nathan Clisby, Yang Shi, Zongzheng Zhou


14:20 Mark Holmes (The University of Melbourne)Alignment percolation (p. 111)

15:10 Nicholas Beaton (The University of Melbourne)Semi-flexible polymers in a strip with attractive walls (p. 110)

15:35 Makoto Narita (National Institute of Technology, Okinawa College)On the global stability of Minkowski spacetimes in string theory (p. 112)

16:00 Ciprian Sorin Acatrinei (National Institute for Nuclear Physics and Engineering)Noncommutative Field Theory and Discrete Orthogonal Polynomials (p. 110)

16:25 Brett Parker (Monash University)The tropological vertex (p. 112)

16:50 Galina Levitina (University of New South Wales)Spectral shift function via regularised determinant of higher order (p. 111)


13:30 Tony Guttmann (The University of Melbourne)Some recent developments in self-avoiding walks (p. 111)

13:55 Abrahim Steve Nasrawi (Monash University)The length of self-avoiding walks on the complete graph (p. 112)

14:20 Seamus Albion (The University of Queensland)Selberg integrals and the AGT conjecture (p. 110)

14:45 Katherine Anne Seaton (La Trobe University)Rolling, rolling, rolling (p. 113)

15:35 Anas Abdur Rahman (The University of Melbourne)Recursions on the Moments of Random Matrix Ensembles (p. 112)

16:00 Allan Trinh (The University of Melbourne)Finite size corrections at the hard edge for the Laguerre β ensemble (p. 113)

16:25 Jiyuan Zhang (The University of Melbourne)Spherical transform and randomised Horn problem (p. 113)

16:50 Peter Forrester (The University of Melbourne)Further random matrix fermi gas analogies (p. 110)

17:15 Mario Kieburg (The University of Melbourne)Matrix products involving Hermitian Random Matrices (p. 111)

17:40 Jesper Ipsen (The University of Melbourne)Large complex systems beyond the instability threshold (p. 111)


13:30 Dinh Tran (The University of Sydney)Hierarchies of q-discrete second, third and fourth Painlevé equations and their properties(p. 113)

25

15. Mathematical Physics, Statistical Mechanics and Integrable systems

13:55 Nalini Joshi (The University of Sydney)Painlev’e VI in Okamoto’s Space (p. 111)

14:20 Pieter Roffelsen (International School for Advanced Studies (SISSA))On the asymptotic distribution of roots of the generalised Hermite polynomials (p. 113)


13:30 Margaret Reid (Swinburne University of Technology)Quantum Entanglement, Schrodinger’s cat, and the Q-function phase-space model of reality(p. 112)

13:55 Thomas Quella (The University of Melbourne)Conformal field theory and the non-abelian SU(2) level k chiral spin liquid (p. 112)

14:20 Alexandr Garbali (The University of Melbourne)A lattice model with the symmetry of the quantum toroidal g l1 algebra (p. 110)

15:10 Laurence Field (Australian National University)Escape estimates for SLE (p. 110)

15:35 Timothy Garoni (Monash University)Critical speeding up in dynamical percolation (p. 110)

16:00 Zongzheng Zhou (Monash University)The coupling time of the Ising Glauber dynamics (p. 114)

26

Special Session 16: Number Theory and AlgebraicGeometry

Organisers Christian Haesemeyer, Liangyi Zhao


13:30 Peng Gao (Beihang University)Lower order terms for the one level density of quadratic Hecke L-functions in the Gaussianfield (p. 115)


15:10 Sean Lynch (UNSW Sydney)The prime ideal theorem in noncommutative arithmetic (p. 116)

15:35 Forrest James Francis (Australian Defence Force Academy)Burgess’ Bound and kth Power Non-residues (p. 115)

16:00 Timothy Trudgian (UNSW Canberra)When primes are just too hard. . . (p. 116)

16:25 Matteo Bordignon (University of New South Wales Canberra)Explicit Pólya-Vinogradov for primitive characters and large moduli (p. 115)

16:50 Aleksander Simonic (University of New South Wales Canberra)On Selberg’s zero density estimate and related results (p. 116)

17:15 Ethan Simpson Lee (UNSW Canberra)On the zero-free region for the Dedekind zeta-function (p. 116)


14:20 Benjamin Moore (The University of Adelaide)Quartic Gauss sums and twisted reciprocity (p. 116)

14:45 Kam Hung Yau (University of New South Wales)A relaxation of Goldbach’s conjecture (p. 117)

15:35 Michaela Cully-Hugill (University of New South Wales Canberra)Explicit results on the sum of a divisor function (p. 115)

16:00 Shehzad Shabbirbhai Hathi (UNSW Canberra)Biases, oscillations, and first sign changes in arithmetic functions (p. 116)

16:25 Ayreena Bakhtawar (La Trobe University)Improvements to Dirichlet’s theorem in Diophantine approximation (p. 115)


13:30 James Borger (Australian National University)The etale fundamental group of semirings (p. 115)

13:55 Thomas Morrill (UNSW Canberra)A combinatoric proof of Jackson’s summation (p. 116)

14:20 Chenyan Wu (The University of Melbourne)Involutive property and irreducibility of theta correspondence (p. 117)

27

Special Session 17: Optimisation

Organisers Andrew Craig Eberhard, Ryan Loxton, Vera Roshchina


17:15 Jie Sun (Curtin University)Stochastic Variational Inequalities, Nash Equilibria under Uncertainty, and the ProgressiveHedging Algorithm (p. 121)


13:30 Alexander Ioffe (Technion, Israel Institute of Technology)On the strong minimum in optimal control. A view from variational analysis. (p. 119)


14:20 Alexander Kruger (Federation University Australia)About the Radius of Metric Subregularity (p. 119)

15:10 Thi Hoa Bui (Federation University Australia)Zero Duality Gap via Abstract Convexity (p. 118)

15:35 Asghar Moeini (Curtin University)Strong Valid Inequalities Identification for Mixed Integer Programs with a given Set ofSolutions (p. 119)

16:00 Cuong Nguyen Duy (Federation University Australia)Characterizations of Robinson regularity properties of implicit multifunctions andapplications (p. 120)

16:25 Neil Kristofer Dizon (The University of Newcastle)Projection algorithms in wavelet construction as a feasibility problem (p. 118)

16:50 Ryan Loxton (Curtin University)Minimizing Control Volatility for Nonlinear Systems with Smooth Input Signals (p. 119)


13:30 Nadia Sukhorukova (Swinburne University of Technology)Remez method applicability in Chebyshev approximation problems (p. 121)

13:55 James Saunderson (Monash University)Certifying polynomial nonnegativity via hyperbolic optimisation (p. 120)

14:20 Scott Boivin Lindstrom (Hong Kong Polytechnic University)On the Projected Polar Proximal Point Algorithm (p. 119)


14:20 Vladimir Gaitsgory (Macquarie University)Linear Programming Based Optimality Conditions for Long Run Average Optimal ControlProblems (p. 118)

15:10 Andrew Craig Eberhard (RMIT University)A Progressive Hedging - Feasibility Pump for Stochastic Integer Programming (p. 118)

15:35 Janosch Rieger (Monash University)A linear programming approach to approximating the infinite time reachable set of strictlystable linear control systems (p. 120)

28

17. Optimisation

16:00 Julien Ugon (Deakin University)Best chebyshev approximation by rational functions (p. 121)

16:25 Vera Roshchina (UNSW Sydney)Optimal selling mechanism design in the presence of budget constraints (p. 120)

29

Special Session 18: Probability Theory and StochasticProcesses

Organisers Andrea Collevecchio, Jie Yen Fan, Giang Nguyen


15:10 Robert Charles Griffiths (Monash University)Forward and Backward in time. Population Genetics Stochastic Process Models (p. 123)


14:20 Angus Hamilton Lewis (The University of Adelaide)Interpretation of approximations to infinitesimal generators as Quasi-Birth-and-Death-likeprocesses (p. 124)

16:00 Han Gan (Northwestern University)Poisson-Dirichlet and Ewens sampling formula approximations for Wright-Fisher models (p.123)

16:25 Alejandro Francisco Ramirez (Catholic University of Chile)Exponential decay for the exit probability from slabs of random walk in randomenvironment (p. 125)

16:50 Zongzheng Zhou (Monash University)Information percolation and the coupling time of the stochastic Ising model (p. 125)

17:15 Andrea Collevecchio (Monash University)Strongly Vertex-Reinforced Jump Processes localizes on 3 points (p. 122)

17:40 adam nie (Australian National University)Weak Subordination of Lévy processes on Hilbert spaces (p. 124)


13:30 Dareen Omari (La Trobe University)Non-central asymptotics for functionals of strong-weak dependent vector random fields (p.125)

13:55 Zdravko Botev (University of New South Wales)Novel Methods for Model Selection in Linear Regression (p. 122)

14:20 Libo Li (University of New South Wales)Positivity Preserving Numerical Schemes for Jump-extended CIR/CEV Process (p. 124)

14:45 Kais Hamza (Monash University)Matching marginals and sums (p. 123)

15:35 Jie Yen Fan (Monash University)Local Brownian Motions (p. 122)

16:00 Kevin Lu (Australian National University)Multivariate Lévy-driven Ornstein-Uhlenbeck processes Using Weak Subordination (p. 124)

16:25 Laurence Field (Australian National University)Brownian motion in multiply connected planar domains (p. 123)

16:50 Illia Donhauzer (La Trobe University)On some asymptotics of functionals of long-range dependent random fields. (p. 122)

17:15 Tareq Alodat (La Trobe University)Limit theorems for filtered long-range dependent random fields (p. 122)

30

18. Probability Theory and Stochastic Processes


13:30 Peter Taylor (The University of Melbourne)A model for cell proliferation in a developing organism (p. 125)

13:55 Fima Klebaner (Monash University)Effect of small noise leading to random initial conditions in dynamical systems (p. 123)

14:20 Andriy Olenko (La Trobe University)Stochastic hyperbolic diffusion equations on the sphere (p. 125)

15:10 Hermanus Marinus Jansen (The University of Queensland)The asymptotic behaviour of the time-varying supermarket model (p. 123)

15:35 Nigel Bean (The University of Adelaide)Yaglom Limit for Stochastic Fluid Models (p. 122)

31

Special Session 19: Representation Theory

Organisers Valentin Buciumas, Ting Xue


16:00 Kari Vilonen (The University of Melbourne)Real Groups, Hodge Theory, and the Langlands duality (p. 128)


13:30 Anna Romanov (The University of Sydney)Contravariant forms on Whittaker modules (p. 128)

13:55 Kevin Coulembier (The University of Sydney)Classification of blocks in category O (p. 127)

14:20 David Ridout (The University of Melbourne)Representations of affine vertex algebras: beyond category O (p. 127)

14:45 Zachary Fehily (The University of Melbourne)Classification of relaxed highest-weight modules for admissible level Bershadsky-Polyakovalgebras (p. 127)

15:35 Masoud Kamgarpour (University of Queensland)Geometric Langlands for Wild Hypergeometric Sheaves (p. 127)

16:50 Linyuan Liu (The University of Sydney)Cohomology of line bundles on flag varieties (p. 127)

17:15 Yusra Naqvi (The University of Sydney)A gallery model for affine flag varieties (p. 127)

17:40 Travis Scrimshaw (The University of Queensland)Crystal structures for canonical Grothendieck functions (p. 128)

32

Special Session 20: Topology

Organisers Diarmuid Crowley, Brett Parker


15:10 Jessica Purcell (Monash University)The triangulation complexity of fibred 3-manifolds (p. 131)


16:00 Boris Lishak (The University of Sydney)Combinatorial isotopies (p. 130)

16:25 Kelly Maggs (The Australian National University)Homotopy Merge Trees in Topological Data Analysis (p. 130)

16:50 Sophie Ham (Monash University)Geometric Triangulations and Highly Twisted Knots (p. 129)

17:15 Craig Hodgson (The University of Melbourne)Constructing geometric structures using twisted tetrahedra (p. 130)


13:30 Daniel Mathews (Monash University)Geometry and physics of circle packings (p. 130)

13:55 Anupam Chaudhuri (Monash University)Local topological recursion governs the enumeration of lattice points in M g ,n (p. 129)

14:20 Mehdi Tavakol (The University of Melbourne)Tautological classes with twisted coefficients (p. 131)

14:45 Ellena Moskovsky (Monash University)On the topological recursion for double Hurwitz numbers (p. 130)

15:35 Csaba Nagy (The University of Melbourne)The Sullivan-conjecture in complex dimension 4 (p. 131)

16:00 Grace Garden (The University of Sydney)The Mapping Class Group Action on the Character Variety of the Once-Punctured Torus (p.129)

16:25 Michael Swaddle (AMSI/University of Melbourne)Airy structures and topological recursion (p. 131)

16:50 Guo Chuan Thiang (The University of Adelaide)T-dualities of orbifolds (p. 132)

17:15 Wee chaimanowong (AMSI/University of Melbourne)Deformation of Curves and Topological Recursions (p. 129)

17:40 Norman Do (Monash University)On the Goulden–Jackson–Vakil conjecture for double Hurwitz numbers (p. 129)


13:30 Marcy Robertson (The University of Melbourne)Modelling homology operations in string topology (p. 131)

33

20. Topology

13:55 Martin Helmer (Australian National University)Complex Linking Numbers for Strata of Varieties (p. 130)

14:20 TriThang Tran (The University of Melbourne)Braids and shuffle algebras (p. 132)

15:10 Xing Gu (AMSI/University of Melbourne)The topological period-index problem (p. 129)

15:35 David Roberts (The University of Adelaide)A descent-theoretic proof of a theorem of Serre (p. 131)

16:00 Paul Norbury (The University of Melbourne)Polynomial relations among kappa classes on the moduli space of curves (p. 131)

34

Tue 3 December 2019

Summary timetable

When What Where09:00–10:30 Opening Ceremony/Prize Giving South 110:30–11:00 Morning tea11:00–12:00 Plenary: Krieger South 112:00–13:30 Lunch13:30–14:20 Plenary: Sikora G8114:20–14:45 6 special session talks Various locations (see below)14:45–15:10 Afternoon Tea15:10–16:00 11 special session talks Various locations (see below)15:35–16:00 7 special session talks Various locations (see below)16:00–16:25 11 special session talks Various locations (see below)16:25–16:50 9 special session talks Various locations (see below)16:50–17:15 10 special session talks Various locations (see below)17:15–17:40 9 special session talks Various locations (see below)17:40–18:05 3 special session talks Various locations (see below)

Special Sessions

3. Applied and Industrial Mathematics189

14:20 Dylan Harries (CSIRO)Applications of temporally regularised matrix factorisations to the analysis of climate data(p. 69)

15:10 Terry O’Kane (CSIRO)Simple Markovian closures for inhomogeneous turbulence (p. 69)

16:00 Samithree Rajapaksha (Monash University)Approximating Link Travel Time Distributions (p. 70)

16:25 Vassili Kitsios (CSIRO)Ensemble transform Kalman filter estimation of thermodynamic parameters in a coupledgeneral circulation model (p. 69)

16:50 Sevvandi Priyanvada Kandanaarachchi (Monash University)DOBIN: dimension reduction for outlier detection (p. 69)

17:15 Lele (Joyce) Zhang (The University of Melbourne)Courier route optimization with unloading bays information and reservation systems (p. 70)

35

Tue 3 December 2019

5. Combinatorics and Graph TheoryG56

14:20 Benjamin Jones (Monash University)Excluded minors for classes of binary functions (p. 76)

15:10 Andrii Arman (Monash University)Generation of random graphs with given degrees (p. 73)

16:00 Rui Zhang (Monash University)Bounded Difference Inequalities for Graph-Dependent Random Variables (p. 78)

16:25 Matthias Fresacher (University of Adelaide)Learning Large Random Graphs Via Group Queries (p. 75)

16:50 Angus Southwell (Monash University)Counting automorphisms of random trees with martingales (p. 77)

17:15 Richard Brak (The University of Melbourne)Universal Bijections for Positive Algebraic Structures (p. 73)

17:40 Kevin Limanta (University of New South Wales)A curious bijection between Dyck paths (p. 76)

9. Functional Analysis, Operator Algebra, Non-commutative Geometry134

15:10 Hai-Long Her (The Australian National University)Fredholm Property of Operators from 2D String Field Theory (p. 89)

15:35 David Leonard Brook (The University of Adelaide)Higher twisted K-theory (p. 89)

16:00 Shaymaa Shawkat Kadhim Al-shakarchi (University of New South Wales)Isomorphisms of AC (σ) spaces. (p. 89)

10. Geometric Analysis and Partial Differential Equations136

14:20 Jesse Gell-Redman (AMSI/University of Melbourne)Global methods for semi-linear hyperbolic equations (p. 92)

15:10 Volker Schlue (The University of Melbourne)On the stability of expanding black hole spacetimes (p. 93)

15:35 Christopher P Rock (UNSW Sydney)Higher-order Cheeger and Buser inequalities, and a dynamics application (p. 93)

16:00 Yilin Ma (The University of Sydney)The Semilinear Calderon Problem on Complex Manifolds (p. 93)

16:25 Florica Corina Cirstea (The University of Sydney)Existence of sharp asymptotic profiles of singular solutions to an elliptic equation with asign-changing nonlinearity (p. 91)

16:50 Yuhan Wu (University of Wollongong)Short time existence for higher order curvature flows with and without boundary conditions(p. 94)

17:15 Nicholas Fewster-Young (University of South Australia)Existence Results for Nonlinear Fractional Differential Equations (p. 92)

17:40 Maria Farcaseanu (The University of Sydney)Singular quasilinear elliptic equations with gradient dependent nonlinearities (p. 92)

11. Geometry including Differential Geometry186

15:10 Artem Pulemotov (The University of Queensland)The prescribed Ricci curvature equation on (SU (2)×SU (2))/U (1)r (p. 96)

15:35 Romina Melisa Arroyo (University of Queensland)On the signature of the Ricci curvature on nilmanifolds (p. 95)

36

Tue 3 December 2019

16:00 Parsa Kavkani (The University of Adelaide)Group Extensions and Bundle Gerbes (p. 95)

16:50 Gerd Schmalz (University of New England)Kähler manifolds, Sasakian manifolds and generalised Taub-NUT solutions (p. 96)

17:15 Jeremy Nugent (University of New South Wales)Superintegrable systems (p. 96)

13. Inclusivity, diversity, and equity in mathematicsG61

15:10 Nalini Joshi (The University of Sydney)A call to action (p. 101)

15:35 Benjamin Burton (University of Queensland)Diversity at the Olympiads: Culture change in elite competition (p. 100)

16:00 Rowena Ball (The Australian National University)Maths on country (p. 100)

16:25 Yudhistira Andersen Bunjamin (UNSW Sydney)Equity considerations and design of mathematics outreach to schools (p. 100)

16:50 Julia Collins (Edith Cowan University)CHOOSEMATHS: approaches to increasing female participation in advanced schoolmathematics (p. 100)

17:15 Valentina-Mira Wheeler (University of Wollongong)Women in mathematics: one perspective on things that work so far and things that could bedone in the future (p. 102)

16. Mathematical Physics, Statistical Mechanics and Integrable systemsG55

14:20 Mark Holmes (The University of Melbourne)Alignment percolation (p. 111)

15:10 Nicholas Beaton (The University of Melbourne)Semi-flexible polymers in a strip with attractive walls (p. 110)

15:35 Makoto Narita (National Institute of Technology, Okinawa College)On the global stability of Minkowski spacetimes in string theory (p. 112)

16:00 Ciprian Sorin Acatrinei (National Institute for Nuclear Physics and Engineering)Noncommutative Field Theory and Discrete Orthogonal Polynomials (p. 110)

16:25 Brett Parker (Monash University)The tropological vertex (p. 112)

16:50 Galina Levitina (University of New South Wales)Spectral shift function via regularised determinant of higher order (p. 111)

17. Number Theory and Algebraic GeometryG57

15:10 Sean Lynch (UNSW Sydney)The prime ideal theorem in noncommutative arithmetic (p. 116)

15:35 Forrest James Francis (Australian Defence Force Academy)Burgess’ Bound and kth Power Non-residues (p. 115)

16:00 Timothy Trudgian (UNSW Canberra)When primes are just too hard. . . (p. 116)

16:25 Matteo Bordignon (University of New South Wales Canberra)Explicit Pólya-Vinogradov for primitive characters and large moduli (p. 115)

16:50 Aleksander Simonic (University of New South Wales Canberra)On Selberg’s zero density estimate and related results (p. 116)

17:15 Ethan Simpson Lee (UNSW Canberra)On the zero-free region for the Dedekind zeta-function (p. 116)

37

Tue 3 December 2019

18. Optimisation188

14:20 Alexander Kruger (Federation University Australia)About the Radius of Metric Subregularity (p. 119)

15:10 Thi Hoa Bui (Federation University Australia)Zero Duality Gap via Abstract Convexity (p. 118)

15:35 Asghar Moeini (Curtin University)Strong Valid Inequalities Identification for Mixed Integer Programs with a given Set ofSolutions (p. 119)

16:00 Cuong Nguyen Duy (Federation University Australia)Characterizations of Robinson regularity properties of implicit multifunctions andapplications (p. 120)

16:25 Neil Kristofer Dizon (The University of Newcastle)Projection algorithms in wavelet construction as a feasibility problem (p. 118)

16:50 Ryan Loxton (Curtin University)Minimizing Control Volatility for Nonlinear Systems with Smooth Input Signals (p. 119)

17:15 Jie Sun (Curtin University)Stochastic Variational Inequalities, Nash Equilibria under Uncertainty, and the ProgressiveHedging Algorithm (p. 121)

19. Probability Theory and Stochastic Processes183

14:20 Angus Hamilton Lewis (The University of Adelaide)Interpretation of approximations to infinitesimal generators as Quasi-Birth-and-Death-likeprocesses (p. 124)

15:10 Robert Charles Griffiths (Monash University)Forward and Backward in time. Population Genetics Stochastic Process Models (p. 123)

16:00 Han Gan (Northwestern University)Poisson-Dirichlet and Ewens sampling formula approximations for Wright-Fisher models (p.123)

16:25 Alejandro Francisco Ramirez (Catholic University of Chile)Exponential decay for the exit probability from slabs of random walk in randomenvironment (p. 125)

16:50 Zongzheng Zhou (Monash University)Information percolation and the coupling time of the stochastic Ising model (p. 125)

17:15 Andrea Collevecchio (Monash University)Strongly Vertex-Reinforced Jump Processes localizes on 3 points (p. 122)

17:40 adam nie (Australian National University)Weak Subordination of Lévy processes on Hilbert spaces (p. 124)

21. Topology137

15:10 Jessica Purcell (Monash University)The triangulation complexity of fibred 3-manifolds (p. 131)

16:00 Boris Lishak (The University of Sydney)Combinatorial isotopies (p. 130)

16:25 Kelly Maggs (The Australian National University)Homotopy Merge Trees in Topological Data Analysis (p. 130)

16:50 Sophie Ham (Monash University)Geometric Triangulations and Highly Twisted Knots (p. 129)

17:15 Craig Hodgson (The University of Melbourne)Constructing geometric structures using twisted tetrahedra (p. 130)

38

Wed 4 December 2019

Summary timetable

When What Where09:00–10:00 Plenary: Joshi G8110:00–10:30 Morning tea10:30–11:30 Plenary: an Huef G8111:30–12:30 Debate G8112:30–13:30 Lunch13:30–13:55 16 special session talks Various locations (see below)13:55–14:20 13 special session talks Various locations (see below)14:20–14:45 15 special session talks Various locations (see below)14:45–15:10 16 special session talks Various locations (see below)15:10–15:35 Afternoon Tea15:35–16:00 14 special session talks Various locations (see below)16:00–16:25 15 special session talks Various locations (see below)16:25–16:50 15 special session talks Various locations (see below)16:50–17:15 15 special session talks Various locations (see below)17:15–17:40 12 special session talks Various locations (see below)17:40–18:05 8 special session talks Various locations (see below)18:05–18:30 1 special session talks Various locations (see below)

Special Sessions

2. AlgebraG58

13:30 Jeroen Schillewaert (University of Auckland)On exceptional Lie geometries (p. 68)

13:55 Subhrajyoti Saha (Monash University)Skeleton groups and their isomorphism problem (p. 67)

14:20 Primoz Moravec (University of Ljubljana)Gaps in probabilities of satisfying some commutator identities (p. 66)

14:45 Michal Ferov (The University of Newcastle)Separating conjugacy classes in wreath products of groups (p. 65)

15:35 Marcos Origlia (Monash University)Simply transitive NIL-affine actions of solvable Lie groups (p. 67)

16:00 Santiago Barrera Acevedo (Monash University)Cocyclic Hadamard matrices of order 4p (p. 65)

16:25 James Mathew Koussas (La Trobe University)Varieties of semiassociative relation algebras (p. 66)

16:50 Lauren Thornton (University of the Sunshine Coast)On properties of descending chains (p. 68)

17:15 Alejandra Garrido (The University of Newcastle)Locally compact topological full groups are locally finite (p. 65)

17:40 Colin David Reid (The University of Newcastle)Locally compact piecewise full groups of homeomorphisms of the Cantor set (p. 67)

39

Wed 4 December 2019

4. Category Theory188

13:30 Richard Garner (Macquarie University)The free tangent category on an affine connection (p. 71)

14:20 Michelle Strumila (The University of Melbourne)Graphical Sets and Mapping Class Groups (p. 72)

14:45 Giacomo Tendas (Macquarie University)Regular Theories Enriched Over Finitary Varieties (p. 72)

15:35 Martina Rovelli (The Australian National University)An embedding of the homotopy theory of 2-categories into that of 2-complicial sets (p. 71)

16:00 Bryce Clarke (Macquarie University)Characterising split opfibrations using lenses (p. 71)

16:25 Bregje Pauwels (The University of Sydney)t-structures and approximable triangulated categories (p. 71)

16:50 David Roberts (The University of Adelaide)Localising by spans and cospans, and functoriality of associated algebras (p. 71)


13:30 Nicholas Cavenagh (University of Waikato)Heffter Arrays with compatible and simple orderings (p. 73)

13:55 Ajani De Vas Gunasekara (Monash University)On determining when small embeddings of partial Steiner triple systems exist (p. 74)

14:20 Adam Gowty (Monash University)New bounds on the maximum size of Sperner partition systems (p. 75)

14:45 Daniel Horsley (Monash University)Generating digraphs with derangements (p. 76)

15:35 Guillermo Pineda-Villavicencio (Deakin University)Minkowski decompositions of polytopes via geometric graphs (p. 77)

16:00 Michael Payne (La Trobe University)Geometric hypergraph colouring problems (p. 77)

16:25 Adam Mammoliti (Monash University)On the Cyclic Matching sequenceablility of regular graphs (p. 76)

16:50 Michael James Gill (Monash University)Perfect 1-factorisations of K16 (p. 75)

17:15 William Crawford (Monash University)Properties of the polytope of polystochastic matrices (p. 74)

17:40 Graham Farr (Monash University)Some problems suggested by the Online Graph Atlas project (p. 74)

6. Computational Mathematics189

13:30 Markus Hegland (Australian National University)Approximating functions of the precision matrix of Gaussian processes (p. 80)

13:55 Gianmarco Manzini (Consiglio Nazionale delle Ricerche (CNR) - Italy)The Virtual Element Method for solving partial differential equations on unstructuredpolytopal meshes (p. 81)

14:45 Hailong Guo (The University of Melbourne)Unfitted Nitsche’s method for computing edge modes in photonic graphene (p. 80)

15:35 Oliver krzysik (Monash University)Parallel time integration of hyperbolic PDEs (p. 80)

16:00 Michael Clarke (UNSW Sydney)Uncertainty Quantification for the Linear Elastic equations (p. 79)

40

Wed 4 December 2019

16:25 El Houssaine QUENJEL (Nice Sophia Antipolis University)A stable finite volume scheme for nonlinear diffusion equations on general 2D meshes (p.81)

16:50 Riya Aggarwal (The University of Newcastle)Bragg Edge Neutron Transmission Strain Tomography using the Finite Element Method (p.79)

17:15 Mark Joseph McGuinness (Victoria University of Wellington)Pressure Buildup in Surtseyan Ejecta (p. 81)

17:40 Janosch Rieger (Monash University)An approach to electrical impedance tomography in unknown domains (p. 81)

18:05 Martin Helmer (Australian National University)Probabilistic Saturations and Alt’s Problem in Mechanism Design (p. 80)

7. Dynamical Systems and Ergodic Theory123

13:30 Anoop Sivasankaran (Khalifa University of Science, Technology)An empirical stability analysis of restricted Four-Body model (p. 85)

13:55 Divahar Jayaraman (The University of Adelaide)Multiscale modelling enables prediction and simulation of floods and tsunamis (p. 84)

14:20 Courtney Rose Quinn (CSIRO)Application of local attractor dimension to reduced space strongly coupled data assimilationfor chaotic multiscale systems (p. 84)

14:45 Sam Jelbart (The University of Sydney)Blowing-up essential singularities in singularly perturbed problems (p. 84)

16:00 Lachlan Smith (The University of Sydney)Model reduction for the collective dynamics of networks of coupled oscillators (p. 85)

16:25 Gary Froyland (University of New South Wales)A spectral approach for quenched limit theorems for random dynamical systems (p. 83)

16:50 Jason Atnip (University of New South Wales)Conformal and Invariant Measures for Random Covering Weighted Systems (p. 83)

17:15 Fawwaz Batayneh (University of Queensland)On the number of ergodic absolutely continuous invariant measures for higher dimensionalrandom dynamical systems (p. 83)

17:40 Cecilia Gonzalez-Tokman (The University of Queensland)Characterization and perturbations of the Lyapunov spectrum of a class of Perron-Frobeniusoperator cocycles (p. 83)

8. Financial mathematics182

13:30 WEI Ning (Monash University)Portfolio optimization with a prescribed terminal wealth density by deep optimal transport(p. 86)

13:55 Ivan Guo (Monash University)Convex duality in robust hedging and optimal stopping problems (p. 86)

14:20 Kihun Nam (Monash University)Non-Markovian Multidimensional Quadratic BSDE (p. 86)

14:45 Kenneth James Palmer (National Taiwan University)Path Independence of Exotic Options and Convergence of Binomial Approximations (p. 87)

15:35 Jan Obloj (University of Oxford)Robust finance: data-driven approach to pricing, hedging and risk management (p. 87)

16:25 Shiyi Wang (Monash University)Calibration of Local-Stochastic Volatility models by Optimal Transport (p. 87)

16:50 James Yang (The University of Sydney)Multiscale Linear-Quadratic Stochastic Optimal Control (p. 87)

41

Wed 4 December 2019

17:15 Edward Kim (The University of Sydney)Vulnerable American Contracts with Extraneous Risks and Market Frictions (p. 86)


13:30 Serena Dipierro (The University of Western Australia)A free boundary problem driven by the biharmonic operator (p. 92)

13:55 Paul Bryan (Macquarie University)Hyperbolic 3-manifolds, embeddings and an invitation to the Cross Curvature Flow (p. 91)

14:20 Julie Clutterbuck (Monash University)The fundamental gap in a negatively curved domain (p. 91)

14:45 Wenhui Shi (Monash University)An epiperimetric inequality approach to the parabolic Signorini problem (p. 94)

15:35 Stephen Lynch (University of Tubingen)A fully nonlinear flow of three-convex hypersurfaces (p. 93)

16:00 Romina Melisa Arroyo (University of Queensland)The prescribed Ricci curvature problem for naturally reductive metrics on compact Liegroups: general theory (p. 91)

16:25 Artem Pulemotov (The University of Queensland)The prescribed Ricci curvature problem for naturally reductive metrics on compact Liegroups: examples (p. 93)

16:50 Valentina-Mira Wheeler (University of Wollongong)Counterexamples to graph preservation under mean curvature flow (p. 94)

17:15 Yong Wei (Australian National University)Horospherically convex geometry in hyperbolic space and geometric flows (p. 94)

12. Harmonic and Semiclassical Analysis134

13:30 Xuan Duong (Macquarie University)Sharp endpoint estimates for Schrödinger groups (p. 98)

13:55 Andrew Hassell (Australian National University)A Fredholm approach to solving semilinear evolution equations (p. 98)

14:20 Alex Amenta (University of Bonn)Vector-valued time-frequency analysis and the bilinear Hilbert transform (p. 98)

14:45 Volker Schlue (The University of Melbourne)Scattering from infinity for semi-linear wave equations with weak null condition (p. 99)

15:35 Hamed Baghal Ghaffari (The University of Newcastle)Construction of Multidimensional Prolate Spheroidal Wave Functions (p. 98)

16:00 Trang Thi Thien Nguyen (University of South Australia)Non-homogeneous T (1) theorem for singular integrals on product quasimetric spaces (p.99)

16:25 Guillermo Javier Flores (Universidad Nacional de Cordoba)Weighted Lebesgue and BMO norm inequalities for the Calderon and Hilbert operators (p.98)

16:50 Fu Ken Ly (The University of Sydney)An improved heat kernel bound for certain magnetic Schrodinger operators. (p. 99)

13. Inclusivity, diversity, and equity in mathematicsG61

13:30 Jessica Purcell (Monash University)WIMSIG resources and initiatives to support careers (p. 102)

13:55 Daniel Mathews (Monash University)Childcare at a large mathematical conference (p. 101)

14:20 Matthew Mack (Multiple Universities)

42

Wed 4 December 2019

Improving accessibility in mathematics (p. 101)

14:45 Jacqui Ramagge (The University of Sydney)Hiring for diversity (p. 102)

15:35 Heather Lonsdale (Curtin University)Creating a critical mass of females in engineering mathematics classrooms (p. 101)

16:00 Collin Grant Phillips (The University of Sydney)Responsive Techniques for Teaching Australian, Indigenous School Students: What PartDoes Culture Play in Teaching Mathematics? (p. 102)

16:25 Asha Rao (Royal Melbourne Institute of Technology)Nurture, gender differences and spatial abilities (p. 102)

16:50 Marcy Robertson (The University of Melbourne)Improving the process of organizing conferences and special semesters (p. 102)

17:15 John Ormerod (The University of Sydney)Descartes was wrong - The psychology of safety and its implications to equality, diversity,and inclusion (p. 101)

14. Mathematical Biology187

13:30 Michael Stumpf (The University of Melbourne)The origins of heavy-tailed laws in biology (p. 105)

14:20 timothy hewson (University of Tasmania)Graded rings of Markov invariants (p. 103)

14:45 Julia Shore (University of Tasmania)The ancient Operational Code is embedded in the amino acid substitution matrix and aaRSphylogenies (p. 105)

15:35 Venta Terauds (University of Tasmania)Symmetry and redundancy: choosing the right algebra for circular genome distancecomputations (p. 105)

16:00 Jeremy Sumner (University of Tasmania)The Markov embedding problem from an algebraic perspective (p. 105)

16:25 Chad Mathew Clark (Western Sydney University)An Algebraic Inversion-Deletion Model for Bacterial Genome Rearrangement (p. 103)

16:50 Joshua Stevenson (University of Tasmania)Investigating rank-based approaches for inferring phylogenies (p. 105)

17:15 Adarsh Kumbhari (The University of Sydney)Emergent signal processing in T cells via regulatory immune mechanisms (p. 104)

17:40 Pantea Pooladvand (The University of Sydney)Modelling the Immune Response of CD4+ T cells: An intimate relationship between T cellsand APCs (p. 104)

15. Mathematics EducationG60

13:30 Poh Hillock (The University of Queensland)Blended learning in a large first year mathematics course (p. 107)

13:55 Simon James (Deakin University)Peer assessment and feedback - in class and online (p. 108)

14:20 Jennifer Palisse (The University of Melbourne)Can Comparative Judgement Improve Student Performance with Rational Inequalities? (p.108)

14:45 Joshua Capel (UNSW Sydney)Learning and Teaching in a Digital world (p. 107)

16:00 Jelena Schmalz (University of New England)Mathematics Enrichment Program at UNE – from Primary School to University (p. 109)

16:25 Renu Choudhary (Auckland University of Technology)

43

Wed 4 December 2019

Empowering, Engaging and Enhancing Students’ Learning using a Pen-Enabled Tablet (p.107)

16:50 Diane Donovan (The University of Queensland)Should I apply for a Teaching Award (p. 107)


13:30 Tony Guttmann (The University of Melbourne)Some recent developments in self-avoiding walks (p. 111)

13:55 Abrahim Steve Nasrawi (Monash University)The length of self-avoiding walks on the complete graph (p. 112)

14:20 Seamus Albion (The University of Queensland)Selberg integrals and the AGT conjecture (p. 110)

14:45 Katherine Anne Seaton (La Trobe University)Rolling, rolling, rolling (p. 113)

15:35 Anas Abdur Rahman (The University of Melbourne)Recursions on the Moments of Random Matrix Ensembles (p. 112)

16:00 Allan Trinh (The University of Melbourne)Finite size corrections at the hard edge for the Laguerre β ensemble (p. 113)

16:25 Jiyuan Zhang (The University of Melbourne)Spherical transform and randomised Horn problem (p. 113)

16:50 Peter Forrester (The University of Melbourne)Further random matrix fermi gas analogies (p. 110)

17:15 Mario Kieburg (The University of Melbourne)Matrix products involving Hermitian Random Matrices (p. 111)

17:40 Jesper Ipsen (The University of Melbourne)Large complex systems beyond the instability threshold (p. 111)


13:30 Peng Gao (Beihang University)Lower order terms for the one level density of quadratic Hecke L-functions in the Gaussianfield (p. 115)

14:20 Benjamin Moore (The University of Adelaide)Quartic Gauss sums and twisted reciprocity (p. 116)

14:45 Kam Hung Yau (University of New South Wales)A relaxation of Goldbach’s conjecture (p. 117)

15:35 Michaela Cully-Hugill (University of New South Wales Canberra)Explicit results on the sum of a divisor function (p. 115)

16:00 Shehzad Shabbirbhai Hathi (UNSW Canberra)Biases, oscillations, and first sign changes in arithmetic functions (p. 116)

16:25 Ayreena Bakhtawar (La Trobe University)Improvements to Dirichlet’s theorem in Diophantine approximation (p. 115)


13:30 Dareen Omari (La Trobe University)Non-central asymptotics for functionals of strong-weak dependent vector random fields (p.125)

13:55 Zdravko Botev (University of New South Wales)Novel Methods for Model Selection in Linear Regression (p. 122)

14:20 Libo Li (University of New South Wales)Positivity Preserving Numerical Schemes for Jump-extended CIR/CEV Process (p. 124)

44

Wed 4 December 2019

14:45 Kais Hamza (Monash University)Matching marginals and sums (p. 123)

15:35 Jie Yen Fan (Monash University)Local Brownian Motions (p. 122)

16:00 Kevin Lu (Australian National University)Multivariate Lévy-driven Ornstein-Uhlenbeck processes Using Weak Subordination (p. 124)

16:25 Laurence Field (Australian National University)Brownian motion in multiply connected planar domains (p. 123)

16:50 Illia Donhauzer (La Trobe University)On some asymptotics of functionals of long-range dependent random fields. (p. 122)

17:15 Tareq Alodat (La Trobe University)Limit theorems for filtered long-range dependent random fields (p. 122)

20. Representation TheoryG62

13:30 Anna Romanov (The University of Sydney)Contravariant forms on Whittaker modules (p. 128)

13:55 Kevin Coulembier (The University of Sydney)Classification of blocks in category O (p. 127)

14:20 David Ridout (The University of Melbourne)Representations of affine vertex algebras: beyond category O (p. 127)

14:45 Zachary Fehily (The University of Melbourne)Classification of relaxed highest-weight modules for admissible level Bershadsky-Polyakovalgebras (p. 127)

15:35 Masoud Kamgarpour (University of Queensland)Geometric Langlands for Wild Hypergeometric Sheaves (p. 127)

16:00 Kari Vilonen (The University of Melbourne)Real Groups, Hodge Theory, and the Langlands duality (p. 128)

16:50 Linyuan Liu (The University of Sydney)Cohomology of line bundles on flag varieties (p. 127)

17:15 Yusra Naqvi (The University of Sydney)A gallery model for affine flag varieties (p. 127)

17:40 Travis Scrimshaw (The University of Queensland)Crystal structures for canonical Grothendieck functions (p. 128)

21. Topology137

13:30 Daniel Mathews (Monash University)Geometry and physics of circle packings (p. 130)

13:55 Anupam Chaudhuri (Monash University)Local topological recursion governs the enumeration of lattice points in M g ,n (p. 129)

14:20 Mehdi Tavakol (The University of Melbourne)Tautological classes with twisted coefficients (p. 131)

14:45 Ellena Moskovsky (Monash University)On the topological recursion for double Hurwitz numbers (p. 130)

15:35 Csaba Nagy (The University of Melbourne)The Sullivan-conjecture in complex dimension 4 (p. 131)

16:00 Grace Garden (The University of Sydney)The Mapping Class Group Action on the Character Variety of the Once-Punctured Torus (p.129)

16:25 Michael Swaddle (AMSI/University of Melbourne)Airy structures and topological recursion (p. 131)

16:50 Guo Chuan Thiang (The University of Adelaide)T-dualities of orbifolds (p. 132)

45

Wed 4 December 2019

17:15 Wee chaimanowong (AMSI/University of Melbourne)Deformation of Curves and Topological Recursions (p. 129)

17:40 Norman Do (Monash University)On the Goulden–Jackson–Vakil conjecture for double Hurwitz numbers (p. 129)

46

Thu 5 December 2019

Summary timetable

When What Where09:00–10:00 Plenary: Ulcigrai G8110:00–10:30 Morning tea10:30–11:30 Plenary: Steinberg G8111:30–12:30 Plenary: Trudgian G8112:30–13:30 Lunch13:30–13:55 11 special session talks Various locations (see below)13:55–14:20 11 special session talks Various locations (see below)14:20–14:45 10 special session talks Various locations (see below)14:45–15:10 Afternoon Tea15:10–16:00 Plenary: Rylands G8116:00–17:15 AGM G81

Special Sessions

2. AlgebraG58

13:30 Amnon Neeman (Australian National University)Non Fourier-Mukai functors (p. 67)

13:55 Robert McDougall (University of the Sunshine Coast)Interpreting a radical theory identity for classes of associative rings (p. 66)

14:20 Abdullahi Umar (Khalifa University of Science, Technology)Some Remarks on monoids of contraction mappings of a finite chain (p. 68)


13:30 Amin Sakzad (Monash University)Middle Product Learning With Errors (p. 77)

13:55 Lynn Batten (Deakin University)How generic ring algorithms and labelled binary trees helped solve an outstanding factoringproblem in number theory. (p. 73)

14:20 Andrea Burgess (University of New Brunswick)The firebreak problem (p. 73)

6. Computational Mathematics189

13:30 Thanh Tran (University of New South Wales)A posteriori error estimation for nonlinear elliptic equations (p. 82)

13:55 Jerome Droniou (Monash University)High-order numerical schemes for degenerate elliptic equations (p. 79)

14:20 Quoc Thong Le Gia (University of New South Wales)A multiscale radial basis function method for severely ill-posed problems on spheres (p. 80)

47

Thu 5 December 2019

7. Dynamical Systems and Ergodic Theory123

13:30 Kenneth James Palmer (National Taiwan University)On Sil’nikov saddle-focus homoclinic orbits (p. 84)

13:55 Davide Ravotti (Monash University)A geometric proof of Ratner’s mixing rates for the horocycle flow (p. 85)

14:20 Sean Gasiorek (The University of Sydney)On the Dynamics of Inverse Magnetic Billiards (p. 83)

8. Financial mathematics182

13:30 Libo Li (University of New South Wales)Mean-field stable CIR process (p. 86)

13:55 Anna Aksamit (The University of Sydney)Modelling additional information: filtration enlarged via a marked random time (p. 86)

14:20 Zhou Zhou (The University of Sydney)On the Notions of Equilibria for Time-inconsistent Stopping Problems in Continuous Time(p. 87)


13:30 Benjamin Blake McMillan (The University of Adelaide)Conservation laws and parabolic Monge-Ampere equations (p. 95)

13:55 A. Rod Gover (The University of Auckland)Distinguished curves and integrability in Riemannian and conformal geometry (p. 95)

12. Harmonic and Semiclassical Analysis134

13:30 Lesley Ward (University of South Australia)Product Hardy space theory on spaces of homogeneous type via orthonormal wavelet bases(p. 99)

13:55 Adam Sikora (Macquarie University)Spectral multipliers without semigroup framework and application to random walks (p. 99)

14:20 Ji Li (Macquarie University)Commutators of Cauchy-Szego type integrals for domains in C n with minimal smoothness(p. 98)


13:30 Sukhen Das (Jadavpur University)Study of HIV in-host model through multi-pathways infection under different blockers :local and global analysis (p. 103)

13:55 Nandadulal Nandadulal Bairagi (Jadavpur University)Pattern formation in a reaction-diffusion predator-prey-parasite model with prey infectionunder the influence of ecological and epidemiological parameters (p. 104)

14:20 Dipak Kumar Kesh (Jadavpur University)Role of induced plant volatile and refuge in tritrophic model (p. 104)


13:30 Dinh Tran (The University of Sydney)Hierarchies of q-discrete second, third and fourth Painlevé equations and their properties(p. 113)

13:55 Nalini Joshi (The University of Sydney)Painlev’e VI in Okamoto’s Space (p. 111)

48

Thu 5 December 2019

14:20 Pieter Roffelsen (International School for Advanced Studies (SISSA))On the asymptotic distribution of roots of the generalised Hermite polynomials (p. 113)


13:30 James Borger (Australian National University)The etale fundamental group of semirings (p. 115)

13:55 Thomas Morrill (UNSW Canberra)A combinatoric proof of Jackson’s summation (p. 116)

14:20 Chenyan Wu (The University of Melbourne)Involutive property and irreducibility of theta correspondence (p. 117)

18. Optimisation188

13:30 Nadia Sukhorukova (Swinburne University of Technology)Remez method applicability in Chebyshev approximation problems (p. 121)

13:55 James Saunderson (Monash University)Certifying polynomial nonnegativity via hyperbolic optimisation (p. 120)

14:20 Scott Boivin Lindstrom (Hong Kong Polytechnic University)On the Projected Polar Proximal Point Algorithm (p. 119)

49

Fri 6 December 2019

Summary timetable

When What Where09:00–10:00 Plenary: Giga G8110:00–10:30 Morning tea10:30–11:30 Plenary: Norbury G8111:30–12:30 Plenary: Samotij G8112:30–13:30 Lunch13:30–13:55 11 special session talks Various locations (see below)13:55–14:20 10 special session talks Various locations (see below)14:20–14:45 10 special session talks Various locations (see below)14:45–15:10 Afternoon Tea15:10–15:35 9 special session talks Various locations (see below)15:35–16:00 9 special session talks Various locations (see below)16:00–16:25 5 special session talks Various locations (see below)16:25–16:50 2 special session talks Various locations (see below)

Special Sessions

2. AlgebraG58

13:30 James East (Western Sydney University)Presentations for diagram algebras and categories (p. 65)

13:55 Richard Garner (Macquarie University)Generalising the étale groupoid–complete pseudogroup correspondence (p. 65)

14:20 Tim Stokes (University of Waikato)Demonic composition and inverse semigroups. (p. 68)

15:10 Tomasz Kowalski (La Trobe University)A little beyond wreath and block (p. 66)

15:35 Thomas Quella (The University of Melbourne)Takiff superalgebras and conformal field theory (p. 67)

16:00 Marcel Jackson (La Trobe University)Algebras defined by equations (p. 66)


13:30 Sanming Zhou (The University of Melbourne)The vertex-isoperimetric number of the incidence graphs of unitals and finite projectivespaces (p. 78)

13:55 Greg Markowsky (Monash University)The Cheeger constant for distance-regular graphs. (p. 77)

14:20 Binzhou Xia (The University of Melbourne)Some examples of nonnormal Cayley graphs on nonabelian simple groups (p. 78)

15:10 Joanne Hall (Royal Melbourne Institute of Technology)Constructions of Difference Covering Arrays using Skolem sequences (p. 75)

50

Fri 6 December 2019

15:35 Vesa Kaarnioja (University of New South Wales)An improved lower bound on Hong and Loewy’s numbers (p. 76)

16:00 Son Hoang Dau (RMIT University)MaxMinSum Steiner Systems for Access-Balancing in Distributed Storage (p. 74)

16:25 Kevin Hendrey (Institute for Basic Science)Covering radius in the Hamming permutation space (p. 75)

9. Functional Analysis, Operator Algebra, Non-commutative Geometry134

13:30 Hendra Gunawan (Bandung Institute of Technology)Some geometric constants for Morrey spaces (p. 89)

13:55 Roozbeh Hazrat (Western Sydney University)The talented monoid of a directed graph (p. 89)

14:20 Geetika Verma (University of South Australia)Inversion of operator pencils on Banach space using Jordan chains (p. 89)


13:30 Enrico Valdinoci (The University of Western Australia)Nonlocal minimal graphs in the plane are generically sticky (p. 94)

13:55 Zihua Guo (Monash University)Ill-posedness of the Camassa-Holm and related equations in the critical space (p. 92)

14:20 Matthew Kevin Cooper (University of New England)Symmetric biharmonic maps (p. 91)

15:10 Kwok-Kun Kwong (University of Wollongong)Quantitative comparison theorems in geometry (p. 92)

15:35 Sevvandi Priyanvada Kandanaarachchi (Monash University)Singularities of Axially Symmetric Volume Preserving Mean Curvature Flow (p. 92)


13:30 Yuri Nikolayevsky (La Trobe University)On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space (p. 96)

13:55 Andreas Vollmer (University of New South Wales)Second order superintegrable systems in arbitrary dimension (p. 97)

14:20 Krzysztof Krakowski (Cardinal Stefan Wyszynski University in Warsaw)Rolling Symmetric Spaces (p. 95)

15:10 Marcos Origlia (Monash University)Locally conformal Käler or symplectic structures on compact solvmanifolds (p. 96)

15:35 Owen Dearricott (The University of Melbourne)Positive curvature in dimension seven (p. 95)


13:30 Andrew Francis (Western Sydney University)The space of tree-based phylogenetic networks (p. 103)

13:55 Lucy Ham (The University of Melbourne)Extrinsic noise and heavy-tailed distributions in gene expression (p. 103)

51

Fri 6 December 2019

15. Mathematics EducationG60

13:30 Jennifer Palisse (The University of Melbourne)Making the Grade: Do Mathematics Marks Matter to Women in STEM (p. 108)

13:55 Jonathan Kress (University of New South Wales)Assessment in First Year Mathematics (p. 108)

14:20 Donald Shearman (Western Sydney University)Does the Effectiveness of Mathematics and Statistics Support Depend on Students’Mathematical Background? (p. 109)

15:10 Deborah Jackson (La Trobe University)Igniting interest, inspiration, investigation and intrigue within mathematics support. (p. 107)

15:35 Terence Mills (La Trobe University)Can Kuhn revolutionise mathematics teaching? (p. 108)


13:30 Margaret Reid (Swinburne University of Technology)Quantum Entanglement, Schrodinger’s cat, and the Q-function phase-space model of reality(p. 112)

13:55 Thomas Quella (The University of Melbourne)Conformal field theory and the non-abelian SU(2) level k chiral spin liquid (p. 112)

14:20 Alexandr Garbali (The University of Melbourne)A lattice model with the symmetry of the quantum toroidal g l1 algebra (p. 110)

15:10 Laurence Field (Australian National University)Escape estimates for SLE (p. 110)

15:35 Timothy Garoni (Monash University)Critical speeding up in dynamical percolation (p. 110)

16:00 Zongzheng Zhou (Monash University)The coupling time of the Ising Glauber dynamics (p. 114)

18. Optimisation188

13:30 Alexander Ioffe (Technion, Israel Institute of Technology)On the strong minimum in optimal control. A view from variational analysis. (p. 119)

14:20 Vladimir Gaitsgory (Macquarie University)Linear Programming Based Optimality Conditions for Long Run Average Optimal ControlProblems (p. 118)

15:10 Andrew Craig Eberhard (RMIT University)A Progressive Hedging - Feasibility Pump for Stochastic Integer Programming (p. 118)

15:35 Janosch Rieger (Monash University)A linear programming approach to approximating the infinite time reachable set of strictlystable linear control systems (p. 120)

16:00 Julien Ugon (Deakin University)Best chebyshev approximation by rational functions (p. 121)

16:25 Vera Roshchina (UNSW Sydney)Optimal selling mechanism design in the presence of budget constraints (p. 120)


13:30 Peter Taylor (The University of Melbourne)A model for cell proliferation in a developing organism (p. 125)

13:55 Fima Klebaner (Monash University)Effect of small noise leading to random initial conditions in dynamical systems (p. 123)

52

Fri 6 December 2019

14:20 Andriy Olenko (La Trobe University)Stochastic hyperbolic diffusion equations on the sphere (p. 125)

15:10 Hermanus Marinus Jansen (The University of Queensland)The asymptotic behaviour of the time-varying supermarket model (p. 123)

15:35 Nigel Bean (The University of Adelaide)Yaglom Limit for Stochastic Fluid Models (p. 122)

21. Topology137

13:30 Marcy Robertson (The University of Melbourne)Modelling homology operations in string topology (p. 131)

13:55 Martin Helmer (Australian National University)Complex Linking Numbers for Strata of Varieties (p. 130)

14:20 TriThang Tran (The University of Melbourne)Braids and shuffle algebras (p. 132)

15:10 Xing Gu (AMSI/University of Melbourne)The topological period-index problem (p. 129)

15:35 David Roberts (The University of Adelaide)A descent-theoretic proof of a theorem of Serre (p. 131)

16:00 Paul Norbury (The University of Melbourne)Polynomial relations among kappa classes on the moduli space of curves (p. 131)

53

List of Registrants

Current as of Fri 22 Nov 2019

Dr Ciprian Sorin Acatrinei National Institute for Nuclear Physics and EngineeringMs Riya Aggarwal (S) The University of NewcastleDr Anna Aksamit The University of SydneyMrs Shaymaa Shawkat Al-shakarchi (S) University of New South WalesMr Seamus Albion (S) The University of QueenslandDr Amie Albrecht University of South AustraliaMr Samuel Bruce Allan (S) University of the Sunshine CoastMr Tareq Alodat (S) La Trobe UniversityDr Alex Amenta University of BonnProf Astrid an Huef Victoria University of WellingtonDr Andrii Arman Monash UniversityDr Romina Melisa Arroyo University of QueenslandDr Jason Atnip University of New South WalesMr Hamed Baghal Ghaffari (S) The University of NewcastleMiss Ayreena Bakhtawar (S) La Trobe UniversityAssoc Prof Rowena Ball The Australian National UniversityDr Santiago Barrera Acevedo Monash UniversityDr Loretta Bartolini Springer-VerlagMr Fawwaz Batayneh (S) University of QueenslandProf Lynn Batten Deakin UniversityProf Nigel Bean The University of AdelaideDr Nicholas Beaton The University of MelbourneProf Jon Berrick The University of SydneyMr Abhishek Bhardwaj (S) Australian National UniversityDr Burzin Bhavnagri Monash UniversityMr Matteo Bordignon (S) University of New South Wales CanberraDr James Borger Australian National UniversityDr Zdravko Botev University of New South WalesMs Elizabeth Bradford (S) University of South AustraliaDr Richard Brak The University of MelbourneMr Jack Brand (S) Australian Mathematical Sciences InstituteProf Philip Broadbridge La Trobe UniversityMr David Leonard Brook (S) The University of AdelaideMr Paul Bryan Macquarie UniversityDr Valentin Buciumas The University of QueenslandDr Pascal R Buenzli Queensland University of TechnologyMs Thi Hoa Bui (S) Federation University AustraliaMr Yudhistira Andersen Bunjamin (S) UNSW SydneyDr Andrea Burgess University of New BrunswickProf Benjamin Burton University of QueenslandDr Joshua Capel UNSW SydneyDr Nicholas Cavenagh University of WaikatoMr Wee chaimanowong (S) AMSI/University of MelbourneMiss Su Yuan Chan (S) Deakin UniversityMiss Ting-Ying Chang (S) University of New EnglandMr Anupam Chaudhuri (S) Monash UniversityDr Renu Choudhary Auckland University of TechnologyAssoc Prof Florica Corina Cirstea The University of SydneyMr Chad Mathew Clark (S) Western Sydney University

54

List of Registrants

Mr Bryce Clarke (S) Macquarie UniversityMr Michael Clarke (S) UNSW SydneyDr Nathan Clisby Swinburne University of TechnologyDr Julie Clutterbuck Monash UniversityDr Andrea Collevecchio Monash UniversityDr Julia Collins Edith Cowan UniversityDr Michael Coons The University of NewcastleDr Matthew Kevin Cooper University of New EnglandDr Kevin Coulembier The University of SydneyDon Coutts Canberra Institute of TechnologyMr William Crawford (S) Monash UniversityDr Anthony Cronin University College DublinMx Diarmuid Crowley The University of MelbourneMs Michaela Cully-Hugill (S) University of New South Wales CanberraMr Kaustav Das (S) Monash UniversityProf Sukhen Das Jadavpur UniversityDr Son Hoang Dau RMIT UniversityProf Jan De Gier The University of MelbourneMs Ajani De Vas Gunasekara (S) Monash UniversityDr Owen Dearricott The University of Melbourne / La Trobe UniversityDr H. Kumudini Dharmadasa University of TasmaniaDr Heiko Dietrich Monash UniversityAssoc Prof Serena Dipierro The University of Western AustraliaMr Neil Kristofer Dizon (S) The University of NewcastleDr Norman Do Monash UniversityMr Illia Donhauzer (S) La Trobe UniversityProf Diane Donovan The University of QueenslandDr James Dowty The University of MelbourneAssoc Prof Jerome Droniou Monash UniversityProf Xuan Duong Macquarie UniversityDr James East Western Sydney UniversityProf Andrew Craig Eberhard RMIT UniversityDr Vladimir Ejov Flinders UniversityMr Patrick Elliott (S) The University of MelbourneProf Andreas Ernst Monash UniversityMs Jie Yen Fan Monash UniversityDr Maria Farcaseanu The University of SydneyProf Graham Farr Monash UniversityZachary Fehily (S) The University of MelbourneDr Michal Ferov The University of NewcastleProf Lilia Ferrario Australian National UniversityMr Nicholas Fewster-Young University of South AustraliaDr Laurence Field Australian National UniversityDr Guillermo Javier Flores Universidad Nacional de CordobaDr Chi-Kwong Fok The University of AucklandProf Peter Forrester The University of MelbourneProf Andrew Francis Western Sydney UniversityMr Forrest James Francis (S) Australian Defence Force AcademyAssoc Prof Federico Frascoli Swinburne University of TechnologyMr Matthias Fresacher (S) University of AdelaideProf Gary Froyland University of New South WalesProf Vladimir Gaitsgory Macquarie UniversityAssoc Prof Linda Galligan University of Southern QueenslandDr Han Gan Northwestern UniversityProf Peng Gao Beihang UniversityDr Alexandr Garbali The University of MelbourneMs Grace Garden (S) The University of SydneyDr Richard Garner Macquarie UniversityAssoc Prof Timothy Garoni Monash University

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List of Registrants

Dr Alejandra Garrido The University of NewcastleDr Sean Gasiorek The University of SydneyDr Jesse Gell-Redman AMSI/University of MelbourneDr Alexandru Ghitza The University of MelbourneDr Mi-Ho Giga University of TokyoProf Yoshikazu Giga University of TokyoMr Michael James Gill (S) Monash UniversityDr Cecilia Gonzalez-Tokman The University of QueenslandProf A. Rod Gover The University of AucklandMr Adam Gowty (S) Monash UniversityMrs Charles Gray (S) La Trobe UniversityProf Robert Charles Griffiths Monash UniversityDr Jens Grimm (S) Monash UniversityProf Joseph Grotowski The University of QueenslandDr Xing Gu AMSI/University of MelbourneProf Hendra Gunawan Bandung Institute of TechnologyDr Hailong Guo The University of MelbourneDr Ivan Guo Monash UniversityMr Zihua Guo Monash UniversityProf Tony Guttmann The University of MelbourneProf Christian Haesemeyer The University of MelbourneMs Anna Haley Monash UniversityDr Joanne Hall Royal Melbourne Institute of TechnologyDr Lucy Ham The University of MelbourneMs Sophie Ham (S) Monash UniversityDr Andy Hammerlindl Monash UniversityMr Jayden Hammet (S) Monash UniversityAssoc Prof Kais Hamza Monash UniversityDr Dylan Harries CSIROAssoc Prof David Harvey University of New South WalesProf Andrew Hassell Australian National UniversityMr Shehzad Shabbirbhai Hathi (S) UNSW CanberraDr Daniel Hauer The University of SydneyMx Eli Hazel (S) Macquarie UniversityProf Roozbeh Hazrat Western Sydney UniversityProf Markus Hegland Australian National UniversityDr Martin Helmer Australian National UniversityDr Kevin Hendrey Institute for Basic ScienceMr Edmund Xian Chen Heng (S) Australian National UniversityProf Bruce Henry University of New South WalesProf Hai-Long Her The Australian National UniversityMr timothy hewson (S) University of TasmaniaDr Poh Hillock The University of QueenslandDr Craig Hodgson The University of MelbourneAssoc Prof Mark Holmes The University of MelbourneDr Daniel Horsley Monash UniversitySeyed Soheil Hosseini (S) Monash UniversityDr Algy Howe Australian National UniversityDr Mumtaz Hussain La Trobe UniversityProf Alexander Ioffe Technion, Israel Institute of TechnologyDr Jesper Ipsen The University of MelbourneDr Deborah Jackson La Trobe UniversityDr Marcel Jackson La Trobe UniversityDr Simon James Deakin UniversityMr Hermanus Marinus Jansen The University of QueenslandMr Divahar Jayaraman (S) The University of AdelaideMr Sam Jelbart (S) The University of SydneyMrs Sangeeta Jhanjee (S) Monash UniversityMr Benjamin Jones (S) Monash University

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List of Registrants

Prof Nalini Joshi The University of SydneyDr Vesa Kaarnioja University of New South WalesDr Nina Kamcev Monash UniversityDr Masoud Kamgarpour University of QueenslandDr Sevvandi Priyanvada Kandanaarachchi Monash UniversityMr Parsa Kavkani (S) The University of AdelaideProf Dipak Kumar Kesh Jadavpur UniversityDr Mario Kieburg The University of MelbourneMr Edward Kim (S) The University of SydneyAssoc Prof Deborah King The University of MelbourneDr Vassili Kitsios CSIROProf Fima Klebaner Monash UniversityProf Sung-Eun Koh Konkuk Univ.Mr James Mathew Koussas (S) La Trobe UniversityDr Tomasz Kowalski La Trobe UniversityDr Krzysztof Krakowski Cardinal Stefan Wyszynski University in WarsawAssoc Prof Jonathan Kress University of New South WalesDr Holly Krieger University of CambridgeProf Alexander Kruger Federation University AustraliaMr Oliver krzysik (S) Monash UniversityMr Adarsh Kumbhari (S) The University of SydneyDr Kwok-Kun Kwong University of WollongongDr Ramiro Augusto Lafuente The University of QueenslandDr Quoc Thong Le Gia University of New South WalesMr Ethan Simpson Lee (S) UNSW CanberraDr Galina Levitina University of New South WalesMr Angus Hamilton Lewis (S) The University of AdelaideDr Ji Li Macquarie UniversityLibo Li University of New South WalesMr Kevin Limanta (S) University of New South WalesDr Scott Boivin Lindstrom Hong Kong Polytechnic UniversityDr Boris Lishak The University of SydneyDr Linyuan Liu The University of SydneyDr Heather Lonsdale Curtin UniversityProf Ryan Loxton Curtin UniversityKevin Lu Australian National UniversityDr Fu Ken Ly The University of SydneyMr Michael Lydeamore (S) Monash UniversityMr Sean Lynch (S) UNSW SydneyStephen Lynch (S) University of TubingenMr Yilin Ma (S) The University of SydneyMr Matthew Mack Multiple UniversitiesDr Barbara Maenhaut The University of QueenslandMr Kelly Maggs (S) The Australian National UniversityMr Adam Mammoliti Monash UniversityDr Gianmarco Manzini Consiglio Nazionale delle Ricerche (CNR) - ItalyDr Greg Markowsky Monash UniversityDr Daniel Mathews Monash UniversityDr Nick McConnell Defence Science and Technology GroupDr Robert McDougall University of the Sunshine CoastProf Mark Joseph McGuinness Victoria University of WellingtonDr Benjamin Blake McMillan The University of AdelaideDr Joel Miller La Trobe UniversityProf Terence Mills La Trobe UniversityDr Asghar Moeini (S) Curtin UniversityMr Benjamin Moore (S) The University of AdelaideProf Primoz Moravec University of LjubljanaDr Thomas Morrill UNSW CanberraProf Sid Morris Federation University Australia

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List of Registrants

Miss Ellena Moskovsky (S) Monash UniversityMr Csaba Nagy (S) The University of MelbourneDr Kihun Nam Monash UniversityProf Nandadulal Nandadulal Bairagi Jadavpur UniversityProf Nandadulal Nandadulal Bairagi University of CalcuttaDr Yusra Naqvi The University of SydneyProf Makoto Narita National Institute of Technology, Okinawa CollegeMr Abrahim Steve Nasrawi (S) Monash UniversityProf Amnon Neeman Australian National UniversityDr Giang Nguyen The University of AdelaideDr Minh Nguyen Monash UniversityMs Trang Thi Thien Nguyen (S) University of South AustraliaMr Cuong Nguyen Duy (S) Federation University AustraliaMr adam nie (S) Australian National UniversityDr Yuri Nikolayevsky La Trobe UniversityMiss WEI Ning (S) Monash UniversityProf Paul Norbury The University of MelbourneMr Jeremy Nugent (S) University of New South WalesDr Terry O’Kane CSIRODr Greg Oates University of TasmaniaProf Jan Obloj University of OxfordMr Peter Olanipekun (S) Monash UniversityDr Andriy Olenko La Trobe UniversityDr Todd Oliynyk Monash UniversityMrs Dareen Omari (S) La Trobe UniversityJordan Orchard (S) Swinburne University of TechnologyDr Marcos Origlia Monash UniversityDr John Ormerod The University of SydneyMr Kieran Emmett OLoughlin (S) The University of AdelaideMx Jennifer Palisse (S) The University of MelbourneProf Kenneth James Palmer National Taiwan UniversityMs Xueyu Pan (S) Monash UniversityDr Brett Parker Monash UniversityDr Bregje Pauwels The University of SydneyDr Michael Payne La Trobe UniversityDr Collin Grant Phillips The University of SydneyDr Guillermo Pineda-Villavicencio Deakin UniversityMx João Vitor Pinto e Silva (S) The University of NewcastleMs Pantea Pooladvand (S) The University of SydneyProf Geoffrey Prince La Trobe UniversityDr Artem Pulemotov The University of QueenslandProf Jessica Purcell Monash UniversityDr Thomas Quella The University of MelbourneDr El Houssaine QUENJEL Nice Sophia Antipolis UniversityDr Courtney Rose Quinn CSIROMr Anas Abdur Rahman (S) The University of MelbourneMrs Samithree Rajapaksha (S) Monash UniversityProf Jacqui Ramagge The University of SydneyProf Alejandro Francisco Ramirez Catholic University of ChileMr Zhenlin Ran (S) The University of NewcastleProf Asha Rao Royal Melbourne Institute of TechnologyDr Davide Ravotti Monash UniversityDr Colin David Reid The University of NewcastleProf Margaret Reid Swinburne University of TechnologyDr David Ridout The University of MelbourneDr Janosch Rieger Monash UniversityDr David Roberts The University of AdelaideDr Marcy Robertson The University of MelbourneMr Christopher P Rock (S) UNSW Sydney

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List of Registrants

Dr Chris Roe RetiredMiss Elisabeth Roesch (S) The University of MelbourneMr Pieter Roffelsen International School for Advanced Studies (SISSA)Dr Anna Romanov The University of SydneyDr Vera Roshchina UNSW SydneyMartina Rovelli The Australian National UniversityAssoc Prof Leanne Rylands Western Sydney UniversityMr Subhrajyoti Saha (S) Monash UniversityDr Amin Sakzad Monash UniversityAssoc Prof Wojciech Samotij Tel Aviv UniversityDr Alba Santin Garcia The University of MelbourneDr James Saunderson Monash UniversityDr Jeroen Schillewaert University of AucklandDr Volker Schlue The University of MelbourneProf Gerd Schmalz University of New EnglandDr Jelena Schmalz University of New EnglandDr Travis Scrimshaw The University of QueenslandDr Katherine Anne Seaton La Trobe UniversityDr Nir sharon Tel Aviv UniversityMr Donald Shearman Western Sydney UniversityMs Wenhui Shi Monash UniversityMrs Julia Shore (S) University of TasmaniaProf Harvinder Sidhu University of New South WalesDr Leesa Sidhu University of New South Wales CanberraDr Adam Sikora Macquarie UniversityDr Joanna Sikora Australian National UniversityMr Aleksander Simonic (S) University of New South Wales CanberraDr Anoop Sivasankaran Khalifa University of Science, TechnologyDr Lachlan Smith The University of SydneyMr Angus Southwell (S) Monash UniversityDr Belinda Spratt Queensland University of TechnologyDr Peter Stacey La Trobe UniversityDr Benjamin Steinberg City University of New YorkMr Joshua Stevenson (S) University of TasmaniaDr Tim Stokes University of WaikatoMs Michelle Strumila (S) The University of MelbourneProf Michael Stumpf The University of MelbourneDr Nadia Sukhorukova Swinburne University of TechnologyDr Jeremy Sumner University of TasmaniaProf Jie Sun Curtin UniversityMr Léon Surel (S) The University of SydneyMichael Swaddle (S) AMSI/University of MelbourneMr Srinibas Swain (S) Monash UniversityDr Thomas Taimre University of QueenslandDr Mehdi Tavakol The University of MelbourneProf Peter Taylor The University of MelbourneMr Stuart Teisseire (S) The University of AdelaideMr Giacomo Tendas (S) Macquarie UniversityDr Venta Terauds University of TasmaniaDr Guo Chuan Thiang The University of AdelaideAssoc Prof Anne Thomas The University of SydneyDr Bevan Thompson The University of QueenslandMiss Lauren Thornton (S) University of the Sunshine CoastDr Dinh Tran The University of SydneyAssoc Prof Thanh Tran University of New South WalesDr TriThang Tran The University of MelbourneMr Allan Trinh (S) The University of MelbourneDr Timothy Trudgian UNSW CanberraDr Ilknur Tulunay UNSW Sydney

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List of Registrants

Dr Julien Ugon Deakin UniversityProf Corinna Ulcigrai University of ZurichDr Abdullahi Umar Khalifa University of Science, TechnologyProf Enrico Valdinoci The University of Western AustraliaMs Shibani Veeraragavan (S) Monash UniversityPaula Verdugo (S) Macquarie UniversityDr Geetika Verma University of South AustraliaProf Kari Vilonen The University of MelbourneDr Andreas Vollmer University of New South WalesShiyi Wang (S) Monash UniversityProf Ian Wanless Monash UniversityAssoc Prof Lesley Ward University of South AustraliaProf Ole Warnaar The University of QueenslandDr Yong Wei Australian National UniversityDr Valentina-Mira Wheeler University of WollongongDr Aaron Wiegand University of the Sunshine CoastDr Tim Wilson Monash UniversityProf David Wood Monash UniversityDr Nicholas Wormald Monash UniversityDr Chenyan Wu The University of MelbourneMs Yuhan Wu (S) University of WollongongDr Binzhou Xia The University of MelbourneDr Ting Xue The University of MelbourneMr James Yang (S) The University of SydneyMr Kam Hung Yau (S) University of New South WalesDr David Yost Federation University AustraliaMr Jiyuan Zhang (S) The University of MelbourneDr Lele (Joyce) Zhang The University of MelbourneMr Rui Zhang (S) Monash UniversityDr Liangyi Zhao University of New South WalesProf Sanming Zhou The University of MelbourneDr Zhou Zhou The University of SydneyDr Zongzheng Zhou Monash University

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Abstracts

1. Plenary 62

Special Sessions2. Algebra 653. Applied and Industrial Mathematics 694. Category Theory 715. Combinatorics and Graph Theory 736. Computational Mathematics 797. Dynamical Systems and Ergodic Theory 838. Financial mathematics 869. Functional Analysis, Operator Algebra, Non-commutative Geometry 89

10. Geometric Analysis and Partial Differential Equations 9111. Geometry including Differential Geometry 9512. Harmonic and Semiclassical Analysis 9813. Inclusivity, diversity, and equity in mathematics 10014. Mathematical Biology 10315. Mathematics Education 10716. Mathematical Physics, Statistical Mechanics and Integrable systems 11017. Number Theory and Algebraic Geometry 11518. Optimisation 11819. Probability Theory and Stochastic Processes 12220. Representation Theory 12721. Topology 129

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1. Plenary

1.1. Algebraic systems of isometriesAstrid an Huef (Victoria University of Wellington)

10:30 Wed 4 December 2019 – G81

Prof Astrid an Huef

An isometry on a Hilbert space is a distance-preserving linear transformation. The algebrasgenerated by algebraic systems of isometries aresurprisingly rigid. I will consider examples of suchsystems arising from quasi-lattice ordered groups(G ,P ) where G is a discrete group with a generatingsubmonoid P . There is a partial order on G definedby x ≤ y if and only if x−1 y ∈ P . The pair (G ,P ) isquasi-lattice ordered if all x, y ∈ G with a commonupper bound in P have a least upper bound in P .

Quasi-lattice ordered groups and their operatoralgebras were introduced by Nica in 1992. I willdiscuss some examples of interest, including theBaumslag-Solitar group

G = ⟨a,b : abc = bd a⟩with submonoid P generated by a and b, andThompson’s group F .

1.2. On total variation flow type equationsYoshikazu Giga (University of Tokyo)

09:00 Fri 6 December 2019 – G81

Prof Yoshikazu Giga

The classical total variation flow is the L2 gradientflow of the total variation. The total variation ofa function u is one-Dirichlet energy, i.e.,

∫ |Du|d x.Different from the Dirichlet energy

∫ |Du|2d x/2, theenergy density is singular at the place where theslope of the function u equals zero. Because of thisstructure, its gradient flow is actually nonlocal in thesense that the speed of slope zero part (called a facet)is not determined by infinitesimal quantity. Thus,the definition of a solution itself is a nontrivial issueeven for the classical total variation flow.

Recently, there need to study various types of suchequations. A list of examples includes the total vari-ation map flow as well as the classical total variationflow and its fourth order version in image denoising,crystalline mean curvature flow or fourth order totalvariation flow in crystal growth problems which areimportant models in materials science below rough-ening temperature.

In this talk, we survey recent progress on these equa-tions with special emphasis on a crystalline meancurvature flow whose solvability was left open morethan ten years. We shall give a global-in-time uniquesolvability in the level-set sense. This last well-posedness result is based on my joint work with N.

Požár (Kanazawa University) whose basic idea de-pends on my earlier joint work with M.-H. Giga (TheUniversity of Tokyo) and N. Požár.

1.3. When applied mathematics collided withalgebraNalini Joshi (The University of Sydney)

09:00 Wed 4 December 2019 – G81

Prof Nalini Joshi

Imagine walking from one tile to another on a latticedefined by reflections associate with an affine Cox-eter or Weyl group. Examples include triangular orhexagonal lattices on the plane. Recently, it was dis-covered that translations on such lattices give rise tothe Painlevé equations, which are reductions of in-tegrable systems that are more familiar to appliedmathematicians and mathematical physicists. I willexplain this surprising development through intro-ductory examples and explain the background to thediscovery of continuous and discrete Painlevé equa-tions.

1.4. Unlikely intersections in arithmetic anddynamicsHolly Krieger (University of Cambridge)

11:00 Tue 3 December 2019 – South 1

Dr Holly Krieger

What does it mean for an intersection to be unlikely?I will explain the idea of unlikely intersections inarithmetic and complex dynamics, focusing on theuse of arithmetic height functions in both cases. I’lldiscuss recent progress on these problems, partic-ularly in the dynamical setting, and some relatedopen questions.

1.5. Enumerative geometry via the moduli space ofsuper Riemann surfaces.Paul Norbury (The University of Melbourne)

10:30 Fri 6 December 2019 – G81

Prof Paul Norbury

The space of all conformal structures on a topologi-cal surface, known as the moduli space of Riemannsurfaces, has been studied since Riemann’s thesisin the 19th century. Mumford initiated the calcu-lation of many algebraic topological invariants overthe moduli space in the 1980s, and Witten relatedthese invariants to two dimensional gravity in the1990s. This viewpoint led Witten to a conjecture,proven by Kontsevich, relating a collection of inte-grals over the moduli space to the KdV hierarchy,which allowed their evaluation. In 2004, Mirzakhaniproduced another proof of Witten’s conjecture viathe study of Weil-Petersson volumes of the modulispace using hyperbolic geometry. In this lecture I

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will describe a new collection of integrals over themoduli space of Riemann surfaces also related to theKdV hierarchy. The proof uses an analogue of Mirza-khani’s argument applied to the moduli space of su-per Riemann surfaces due to recent work of Stanfordand Witten. Super Riemann surfaces are essentiallydefined by replacing the field of complex numberswith a Grassman algebra. This appearance of themoduli space of super Riemann surfaces to solve aproblem over the classical moduli space is deep andsurprising.

1.6. The mathematics problemLeanne Rylands (Western Sydney University)

15:10 Thu 5 December 2019 – G81

Assoc Prof Leanne Rylands

The mathematics problem is the inadequate prepa-ration of many new undergraduate students for themathematical demands of their degree.

Many of us complain that too many students arecoming to university under-prepared for the math-ematical and statistical aspects of their studies. Sig-nificant numbers of under-prepared students en-rolling in mathematics subjects can lead to high fail-ure rates. High failure rates are seen as decreasingstudent retention and progression. High failure ratesin mathematics subjects can lead to others blam-ing mathematicians for poor teaching, and might beused to argue for taking mathematics teaching awayfrom mathematicians, which in turn can decreasethe income of mathematics departments.

Mathematics academics have been complaining forseveral decades about the poor standard of new stu-dents. Is the situation really getting worse?

Much has been published about this problem. I willgive an overview of some evidence to demonstratethat overall, students are less mathematically pre-pared than in the past. I will also consider possibleactions.

1.7. Large deviations in random graphsWojciech Samotij (Tel Aviv University)

11:30 Fri 6 December 2019 – G81

Assoc Prof Wojciech Samotij

Suppose that Y1, . . . ,YN are i.i.d. (independent iden-tically distributed) random variables and let X = Y1+·· · +YN . The classical theory of large deviations al-lows one to accurately estimate the probability of thetail events X < (1−c)E[X ] and X > (1+c)E[X ] for anypositive c. However, the methods involved stronglyrely on the fact that X is a linear function of the inde-pendent variables Y1, . . . ,YN . There has been consid-erable interest—both theoretical and practical—indeveloping tools for estimating such tail probabili-ties also when X is a nonlinear function of the Yi .One archetypal example studied by both the com-binatorics and the probability communities is when

X is the number of triangles in the binomial ran-dom graph G(n, p). I will discuss two recent devel-opments in the study of the tail probabilities of thisrandom variable. The talk is based on joint workswith Matan Harel and Frank Mousset and with GadyKozma.

1.8. Advancing women in Australian Mathematics:context, challenges and achievementsJoanna Sikora (Australian National University)

13:30 Tue 3 December 2019 – G81

Dr Joanna Sikora

This talk reviews recent research undertaken bysocial scientists on women in mathematics. First,adopting a life-course perspective it summarisesfindings on the persisting gap in vocational interestin mathematics among adolescent boys and girls,including its potential to widen over time. Sys-tematic differences between boys and girls in thechoice of basic and advanced mathematics for ATAR(Australian Tertiary Admissions Rank) are discussed.Next, the consequences of these choices for tertiaryeducation specialisations and availability of suitablyqualified male and female graduates are considered.

Following this introduction, the talk summarizesresearch on underrepresentation of women inmathematics departments in Australia and acrossthe world. The focus is on structural and institu-tional process which, over the course of individualcareers, can amount to significant disadvantageeven in the absence of overt discrimination. Topicsdiscussed include cultural stereotypes that linkperceptions of brilliance and academic talent withmasculinity, gender differences in professionalcapital, i.e. peer esteem, accorded to male andfemale mathematicians, the gender gap in rates ofpublications and impact, documented bias in stu-dent evaluations and factors that enable success inestablishing international collaborations. The talkconcludes by summarizing the literature on practi-cal steps that managers, or heads of departments,could take to improve gender equity.

1.9. Monoids in Representation Theory, MarkovChains, Combinatorics and Operator AlgebrasBenjamin Steinberg (City University of New York)

10:30 Thu 5 December 2019 – G81

Dr Benjamin Steinberg

Monoids form a natural model of irreversible phe-nomena and as such arise in several areas of mathe-matics. For example, finite state Markov chains canalways be viewed as random walks of finite monoidson finite sets. Sometimes the representation the-ory of monoids can be used to successfully analyzethe Markov chain. The representation theory of fi-nite monoids, however, is much more complicatedthan the group case, which leads to interactions with

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the modern representation theory of finite dimen-sional algebras (e.g., quivers, quasi-hereditary alge-bras, etc.).

Monoids also appear in many guises in combina-torics. The faces of a central hyperplane arrange-ment, or more generally an oriented matroid, carrya natural monoid structure. The representation the-ory of the monoid is intimately connected with theunderlying combinatorial structure. For instancethe Möbius function of the geometric lattice of theunderlying matroid is encoded in the Cartan ma-trix of the associated monoid algebra. Similar semi-group structures can be found in other geometricobjects such as finite CAT(0) cube complexes.

In the theory of operator algebras, C∗-algebras gen-erated by partial isometries play a crucial role, par-ticularly for groupoid C∗-algebras. Such algebrasare quotients of inverse semigroup algebras and thishas led to a fruitful interplay between analysis, semi-group theory and the theory of groupoids. Some ofthe same ideas used in the representation theory offinite monoids have implications for groupoid C∗-algebras and their associated discrete analogues.

In this talk we will survey some of the surprisingways in which algebras associated to semigroups ormonoids appear in mathematics and can be used tosolve problems coming from outside of monoid the-ory.

1.10. Primes = Hard +O(1)Timothy Trudgian (UNSW Canberra)

11:30 Thu 5 December 2019 – G81

Dr Timothy Trudgian

Suppose I give you the inequality n2+9 ≤ 2n2, wheren is some natural number. Clearly, this is true forall sufficiently large n: there are only finitely manyexceptions, that is O(1) exceptions. In this case wecan simply enumerate the exceptions: n = 1 and n =2, and wait for the Fields Medal Committee to comeknocking.

We have known, for over 80 years, that there are O(1)odd numbers N that cannot be written as the sum ofthree primes. But, unlike the above inequality, enu-merating the exceptions proved very difficult. Oh,sure, N = 1,3,5 cannot be written as the sum of threeprimes, but even as late as the 2000s we only knewthat there were no other exceptions beyond 101347.That’s a big O(1)!

I shall outline some problems in number theory thathave the flavour of the above examples, and mentionsome modern progress on some hard, old problems.

1.11. Shearing and mixing in surface flowsCorinna Ulcigrai (University of Zurich)

09:00 Thu 5 December 2019 – G81

Prof Corinna Ulcigrai

Flows on surfaces describe many systems of physicalorigin and are one of the most fundamental exam-ples of dynamical systems, studied since Poincare’.In the last decade, there have been a lot of advancesin our understanding of the chaotic properties ofsmooth area-preserving flows (a class which includelocally Hamiltonian flows). In the talk we will mo-tivate and survey some of the recent breakthroughsand the mechanisms, such as shearing, on whichthey are based, which exploit analytic, arithmeticand geometric techniques.

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2. Algebra

2.1. Cocyclic Hadamard matrices of order 4pSantiago Barrera Acevedo (Monash University)

16:00 Wed 4 December 2019 – G58

Santiago Barrera Acevedo, Padraig Ó Catháin and Heiko

Dietrich

Cocyclic Hadamard matrices were introduced by deLauney and Horadam as a class of Hadamard ma-trices with interesting algebraic properties. Catháinand Röder described a classification algorithm forcocyclic Hadamard matrices of order 4n based onrelative difference sets in groups of order 8n; this ledto the classification of cocyclic Hadamard matricesof order at most 36. Based on work of de Launeyand Flannery, we investigated in detail the structureof cocyclic Hadamard matrices of order 4p, with pprime. This led to a classification algorithm and thedetermination of cocyclic Hadamard matrices of or-ders 44 and 52 up to equivalence.

2.2. Presentations for diagram algebras andcategoriesJames East (Western Sydney University)

13:30 Fri 6 December 2019 – G58

Dr James East

A presentation for an algebraic structure (e.g., agroup, ring or lattice) consists of:

(1) generators, out of which each element canbe built using the algebraic operations;and

(2) relations, from which all relationships be-tween the generators can be deduced.

Presentations are very useful for a number of rea-sons. For one thing, you can define an action of yourstructure by specifying how the generators act, andthen checking that the relations are preserved; thisis especially helpful when the structure is complex,and the generators relatively simple.

This talk will discuss some techniques for actuallyobtaining presentations in the first place. It will fo-cus primarily on diagram algebras and categories(including partition, Brauer and Temperley-Lieb),but the techniques apply to many more. In eachcase, the starting point is an associated diagrammonoid, from which the algebras and categories canbe built via a natural twisting construction.

2.3. Separating conjugacy classes in wreathproducts of groupsMichal Ferov (The University of Newcastle)

14:45 Wed 4 December 2019 – G58

Dr Michal Ferov

(join work with M. Pengitore) A natural way of study-ing groups is via studing their finite quotients. A

group is said to be conjugacy separable if for ev-ery pair of non-conjugate elements there exists a fi-nite group and surjective homomorphism onto thesaid group such that the images of the two elementsremain non-conjugate. We study the behaviour ofconjugacy separability with respect to the contruc-tuin of wreath products, extending previous workof Remeslennikov. In particular, we classify all p-conjugacy separable wreath producs, i.e. wreathproducts where we only allow finite p-groups as thequotients.

2.4. Generalising the étale groupoid–completepseudogroup correspondenceRichard Garner (Macquarie University)

13:55 Fri 6 December 2019 – G58

Dr Richard Garner

There is a well known correspondence, dating backto the earliest days of sheaf theory, between sheaveson a space X , and local homeomorphisms into X .This correspondence underlies a richer one, be-tween étale groupoids and complete pseudogroups.An étale groupoid is a topological groupoid whosesource map is a local homeomorphism; a completepseudogroup is an inverse monoid S which acts ona space X in such a way as to make S into an X -sheaf. The étale groupoid–complete pseudogroupcorrespondence can be found in embryonic form inwork of Ehresmann, Haefliger and Kellendonk, butreaches its abstract modern expression in work ofResende and Lawson–Lenz.

In this talk, I will explain some joint work with RobinCockett which generalises the étale groupoid–complete pseudogroup correspondence further,along four distinct axes: by replacing inversemonoids by inverse categories; by replacing inversemonoids by restriction monoids; by enhancingthe functoriality of the correspondence; and, mostradically, by working not with topological étalegroupoids, but rather with groupoids internal to asuitable join restriction category. Diverse exampleswill be provided to illustrate the utility of thesegeneralisations.

2.5. Locally compact topological full groups arelocally finiteAlejandra Garrido (The University of Newcastle)

17:15 Wed 4 December 2019 – G58

Dr Alejandra Garrido

Topological (a.k.a. piecewise) full groups havegained much attention in group theory in recentyears as a source of infinite simple groups. They aregroups of homeomorphisms of Cantor space thatare "stitched up" from "pieces" of some given groupof homeomorphism. This general construction can

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be used obtain examples of simple non-discretetotally disconnected locally compact groups. Thereare various choices of group topologies that onecould take. I will report on joint work in progresswith Colin Reid where we show that a piecewise fullgroup which is locally compact with respect to the"obvious" choice of group topology (compact-open)is always locally finite and countable, and we give adescription of these groups.

In case you wonder, there are other topologies thatone can take to obtain non-discrete locally compactpiecewise full groups, but these examples are a storyfor a different talk.

2.6. Algebras defined by equationsMarcel Jackson (La Trobe University)

16:00 Fri 6 December 2019 – G58

Marcel Jackson (speaker) joint work with Peter Higgins

The study of equationally defined classes of alge-braic systems—varieties—has a long history, andcontinues to hold many open problems in semi-group theory. In this context, an equation, or identityis a universally quantified equality between terms.In the present talk we explore the slightly differentlandscape of algebraic systems described by equa-tions with arbitrary quantification: universal or ex-istential, in any combination. This turns out to be auseful language for axiomatically capturing a greatmany natural classes in semigroup theory, includ-ing the e-variety concept introduced by Tom Hallin 1989 for studying classes of regular semigroups.As an illustrative example, one finds that groups areprecisely those semigroups satisfying

∀a,b∃x, y (ax = b & y a = b)

We find that in the lattice of equationally definedclasses of semigroups (in this generalised sense ofequation), the finitely generated atoms are preciselythose equationally defined classes generated by twoelement semigroups and by finite simple groups.

2.7. Varieties of semiassociative relation algebrasJames Mathew Koussas (La Trobe University)

16:25 Wed 4 December 2019 – G58

Mr James Mathew Koussas

It is well known that the subvariety lattice of the vari-ety of relation algebras has exactly three atoms. The(join-irreducible) covers of two of these atoms areknown, but a complete classification of the (join-irreducible) covers of the remaining atom has notyet been found. These statements are also true of arelated subvariety lattice, namely the subvariety lat-tice of the variety of semiassociative relation alge-bras. We will show that this atom has continuummany covers in this subvariety lattice using a previ-ously established term equivalence between a vari-ety of tense algebras and a variety of semiassociativer-algebras.

2.8. A little beyond wreath and blockTomasz Kowalski (La Trobe University)

15:10 Fri 6 December 2019 – G58

Dr Tomasz Kowalski

(Joint work with Michal Botur, Palacky University ofOlomouc, Czechia)

We present a semigroup construction generalisingthe two-sided wreath product. Instead of workingwithin a direct power SX and a K acting on X , wework with a disjoint union of sets I [s] indexed bythe elements of S and a system of maps (λ,ρ) be-tween the sets I [s]. Intuitively and roughly, it is asif we allowed some coordinates from X to drop outfrom time to time, so that, for example, a product(a,b,c,d) · (u, v) can make sense and be equal to(av,b,cu). For any semigroups H and S this leadsto what we call a λρ-product G [S]. We show that:1. G [S] is a group if and only if G and S are; then G [S]

is isomorphic to the usual wreath product.2. For semigroups, the construction is strictly moregeneral than the known constructions; in particular,we can show that every finite semigroup divides aniterated λρ-product whose factors are finite simplegroups and a two-element semilattice.

The first result shows that for groups we do not getanything new. The second shows that for semi-groups we do. The second result, however, uses thefull force of Krohn-Rhodes Theorem, so it is less ex-citing than it may seem.

2.9. Interpreting a radical theory identity forclasses of associative ringsRobert McDougall (University of the Sunshine Coast)

13:55 Thu 5 December 2019 – G58

Dr Robert McDougall

In this talk we describe an identity involving theclass operators U, S and NOT which appear in baseradical theory constructions and interpret its heredi-tary radical class meaning for universal classes of as-sociative rings.

2.10. Gaps in probabilities of satisfying somecommutator identitiesPrimoz Moravec (University of Ljubljana)

14:20 Wed 4 December 2019 – G58

Prof Primoz Moravec

Let w be a non-trivial word in a free group of rankd and w : Gd → G a corresponding word map on afinite group G . Let Pw=1(G) = |w−1(1)|/|G|d be theprobability that a randomly chosen d-tuple of ele-ments of G evaluates to 1 under the map w . Thereis an old result of Gustafson stating that if G is a fi-nite non-abelian group, then the commuting prob-ability P[x,y]=1(G) is bounded above by 5/8. Dixon(2004) posed a question whether or not there existsa constant η < 1 depending on w only such that forevery finite group G not satisfying the law w = 1

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we have that Pw=1(G) ≤ η. We answer the questionaffirmatively for the 2-Engel word w = [x, y, y] andmetabelian word w = [[x, y], [z, w]].

This is joint work with Costantino Delizia and ChiaraNicotera (University of Salerno, Italy), and UrbanJezernik (University of the Basque Country, Spain).

2.11. Non Fourier-Mukai functorsAmnon Neeman (Australian National University)

13:30 Thu 5 December 2019 – G58

Prof Amnon Neeman

We will describe a counterexample, due to Rizzardoand Van den Bergh, saying that not all maps betweenderived categories of smooth projective varieties areFourier-Mukai. I will describe my contribution tothe paper, which produced a vast source of potentialnew examples.

2.12. Simply transitive NIL-affine actions ofsolvable Lie groupsMarcos Origlia (Monash University)

15:35 Wed 4 December 2019 – G58

Dr Marcos Origlia

Every simply connected and connected solvable Liegroup G admits a simply transitive action on a nilpo-tent Lie group H via affine transformations. Al-though the existence is guaranteed, not much isknown about which groups G can act simply transi-tive on which groups H . So far the focus was mainlyon the case where G is also nilpotent.

In this talk, we will discuss the case when G is a solv-able (non-nilpotent) Lie group and H is a nilpotentLie group. This is a work in progress with Jonas Deré(KU Leuven, Belgium).

2.13. Takiff superalgebras and conformal fieldtheoryThomas Quella (The University of Melbourne)

15:35 Fri 6 December 2019 – G58

Dr Thomas Quella

We discuss Takiff superalgebras from the perspectiveof applications in conformal field theory. Takiff su-peralgebras arise from a truncated loop algebra con-struction and the focus of the talk will be on the exis-tence of invariant forms, automorphisms and com-patibility with affinization (the full loop algebra con-struction).

2.14. Locally compact piecewise full groups ofhomeomorphisms of the Cantor setColin David Reid (The University of Newcastle)

17:40 Wed 4 December 2019 – G58

Dr Colin David Reid

Let X be the Cantor set and let Homeo(X) be thegroup of homeomorphisms from X to itself. Say that

a subgroup G of Homeo(X) is piecewise full if, when-ever g in Homeo(X) is such that the action of g canbe specified by a locally constant element of G, thenin fact g is in G.

Piecewise full groups (also called topological fullgroups) have been an active area of research sincethe 1990s, with most authors focusing on the casewhere the group is countable. More recently, piece-wise full groups have emerged as a rich source ofexamples of nondiscrete (hence uncountable) sim-ple locally compact groups, and they have some in-teresting universality properties in the class of to-tally disconnected locally compact groups. I will talkabout some results of ongoing work with A. Garridoand D. Robertson.

2.15. Skeleton groups and their isomorphismproblemSubhrajyoti Saha (Monash University)

13:55 Wed 4 December 2019 – G58

Mr Subhrajyoti Saha

Classification of groups up to isomorphism is oneof the main themes in group theory. A particularchallenge is to understand finite p-groups, that is,groups of p-power order for a prime p. Since a clas-sification of p-groups by order seems out of reach forlarge exponents n, other invariants of groups havebeen used to attempt a classification; a particularlyintriguing invariant is coclass. A finite p-group of or-der pn and nilpotency class c has coclass r = n − c.The investigation of p-groups by coclass has beeninitiated by Leedham-Green and Newman, and nu-merous deep results have been obtained since then.

Recent work in coclass theory is often concernedwith the study of the coclass graph G (p,r ) associatedwith the finite p-groups of coclass r . The vertices ofthe coclass graph G (p,r ) are (isomorphism type rep-resentatives of) the finite p-groups of coclass r , andthere is an edge G → H if and only if G is isomorphicto H/γ(H) where γ(H) is the last non-trivial term ofthe lower central series of H . It is known that largeparts of this infinite graph have periodic patternsand that these patterns are reflected in the structuresof the involved groups. It has also become appar-ent that one of the feasible approaches for investi-gating G (p,r ) is to first focus on so-called skeletongroups. For odd p, let S be an infinite pro-p groupand informally skeleton groups can be described astwisted finite quotients of S, where the twisting is in-duced by some suitable homomorphism. The im-portance of these groups is explained by the deepresult that, with only finitely many exceptions, everygroup G in G (p,r ) has a bounded depth from a skele-ton group. This justifies saying that these groups in-deed form the ‘skeleton’ of G (p,r ). We further inves-tigate when two skeleton groups are isomorphic. Wepresent some results towards this direction includ-ing two interesting cases. During our work we also

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identified a number of gaps in some recent work andwe close these gaps by proving the required results ina more general context.

This is a joint work with Dr. Heiko Dietrich, MonashUniversity, Australia.

2.16. On exceptional Lie geometriesJeroen Schillewaert (University of Auckland)

13:30 Wed 4 December 2019 – G58

Dr Jeroen Schillewaert

Parapolar spaces are point-line geometries intro-duced as a geometric approach to (exceptional) al-gebraic groups. We provide a characterisation of awide class of Lie geometries as parapolar spaces sat-isfying a simple intersection property. In particularmany of the exceptional Lie geometries occur. Infact, our approach unifies and extends several ear-lier characterizations of (exceptional) Lie geometriesarising from spherical Tits-buildings.

(This is joint work with Anneleen De Schepper, Hen-drik Van Maldeghem and Magali Victoor)

2.17. Demonic composition and inversesemigroups.Tim Stokes (University of Waikato)

14:20 Fri 6 December 2019 – G58

Dr Tim Stokes

Most people are familiar with the definition of com-position of two binary relations. This operation gen-eralises composition of functions and is associative.A less well-known operation on relations is so-calleddemonic composition, which is more restricted thanordinary composition, and is of interest because itarises naturally when modelling non-deterministiccomputer programs. Demonic composition is alsoassociative, and also generalises function composi-tion. Why is it so nicely behaved? We show how it fitsinto a much more general framework that applies toBaer ∗-semigroups (such as the multiplicative semi-groups of ∗-regular rings) and beyond. In partic-ular we may define the “demonic product" of twon×n real or complex matrices, which almost alwaysagrees with the usual matrix product but which givesan unexpected inverse semigroup structure on suchmatrices, where inverses are nothing but Moore-Penrose inverses.

2.18. On properties of descending chainsLauren Thornton (University of the Sunshine Coast)

16:50 Wed 4 December 2019 – G58

Miss Lauren Thornton

We give a complete description up to isomorphismof the way descending chains of ideals for universalclass objects in a general setting can terminate withconsequences for structures like groups and rings.We show that while some ideals arise because theysatisfy a condition held by the elements of the class

object, their existence can also be inferred as an out-come of the structural requirements framed by theclass setting.

2.19. Some Remarks on monoids of contractionmappings of a finite chainAbdullahi Umar (Khalifa University of Science,

Technology)

14:20 Thu 5 December 2019 – G58

Dr Abdullahi Umar

A general systematic study of the monoids/semigroupsof partial contractions of a finite chain and theirvarious subsemigroups of order-preserving/order-reversing and/or order-decreasing transformationswas initiated in 2013 supported by a grant from TheResearch Council of Oman (TRC).

Our aim in this talk is to present the results ob-tained so far by the presenter and his co-authorsas well as others. Broadly, speaking the results canbe divided into two groups: algebraic and combi-natorial enumeration. The algebraic results showthat these semigroups are nonregular (left) abun-dant semigroups (for n ≥ 4) whose Green’s relationsadmit a nontrivial characterization. The combina-torial enumeration results show links with Fibonaccinumbers, Motzkin numbers and sequences some ofwhich are in the encyclopedia of integers sequences(OEIS).

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3. Applied and Industrial Mathematics

3.1. Applications of temporally regularised matrixfactorisations to the analysis of climate dataDylan Harries (CSIRO)

14:20 Tue 3 December 2019 – 189

Dr Dylan Harries

A ubiquitous step in analyses of climate data isthe application of an initial dimension reductionmethod to obtain a low-dimensional representationthat retains the relevant features of the data, whilealso being tractable to analyse. Standard methodssuch as principal component analysis (PCA) arehighly efficient for this purpose, but can yield resultsthat are difficult to interpret physically, and relyon assumptions of stationarity and independencethat are generally not satisfied by the data. Oneapproach to rectifying these shortcomings is toconsider alternative factorisations from the broaderclass of matrix decompositions from which PCAarises as a special case. In particular, doing so allowsfor the use of regularisations tailored towards theselection of the most salient features in the datafor a given analysis, and for the explicit modellingof dependence between samples. In this talk, wedemonstrate the application of a recently proposedconvex coding method incorporating temporalregularisations chosen to target the large scale,persistent structures associated with low-frequencyclimate variability, and compare the performance ofthe method with traditional strategies such as PCAand k-means clustering.

3.2. DOBIN: dimension reduction for outlierdetectionSevvandi Priyanvada Kandanaarachchi (Monash

University)

16:50 Tue 3 December 2019 – 189

Dr Sevvandi Priyanvada Kandanaarachchi

Outlier detection is used in diverse applicationsranging from finance to extreme weather condi-tions. A common challenge in outlier detection isthat a data point may be an outlier in the originalhigh dimensional space, but not an outlier in thelow dimensional subspace created by a dimensionreduction method. In this talk, we introduce anew set of basis vectors called DOBIN designedfor outlier detection. DOBIN brings outliers tothe forefront making it easier to detect them. Wedemonstrate DOBIN’s effectiveness using an exten-sive data repository. In addition, we present someinteresting examples of outlier visualization usingDOBIN.

3.3. Ensemble transform Kalman filter estimationof thermodynamic parameters in a coupled generalcirculation modelVassili Kitsios (CSIRO)

16:25 Tue 3 December 2019 – 189

V. Kitsios, P. Sandery, T. J. O’Kane, P. Sakov and R. Fiedler

In climate simulations there are many model pa-rameters that are known with little precision. Thebiases observed in these complex multi-disciplinarymulti-scale simulations can be highly sensitive tothe specification of such parameters. Within a dataassimilation (DA) framework we develop a systemicapproach to estimate such model parameters, withthe intention to reduce model bias and hence im-prove forecast skill.

In general, DA provides the ability to modify imper-fect simulations of reality with a series of incompleteand possibly noisy measurements, ideally resultingin a better estimation of the true system state, andalso potentially an estimate of the model param-eters. For the experiments undertaken within, weadopt the CSIRO Climate Analysis Forecast Ensem-ble system, which employs the ensemble transformKalman filter first proposed by Bishop et. al. (2001),and specifically the implementation of Sakov (2014).The system is run with an ensemble of 96 forwardclimate simulations. The forward model is theGeophysical Fluid Dynamics Laboratory coupledatmospheric, oceanic, and sea-ice climate simulatoras described in Griffies (2012). An earlier iterationof the CAFE system is documented in O’Kane et. al.(2018).

Using this configuration we identify spatio-temporally varying parameters that minimisethe error between short term (daily to weekly) fore-casts of the coupled climate model and a network ofreal world atmospheric, oceanic, and sea-ice obser-vations. The parameters of interest are the surfaceocean albedo, and the ocean penetration depth ofincoming shortwave radiation. These parametersare shown to have a significant impact on the shortterm predictability of the underlying model. Welook to determine if parameters estimated fromwithin a DA training period to optimise many shortterm forecasts, can reduce the onset of model biasin longer term (multi-year) forecasts.

3.4. Simple Markovian closures for inhomogeneousturbulenceTerry O’Kane (CSIRO)

15:10 Tue 3 December 2019 – 189

Drs Terry O’Kane and Jorgen S. Frederiksen

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3. Applied and Industrial Mathematics

Markovian closures for the interaction of two-dimensional inhomogeneous turbulent flows withRossby waves and topography are formulated basedon three variants of the fluctuation dissipation the-orem (FDT) i.e. the current-time (quasi-stationary)FDT, the prior-time (non-stationary) FDT and thecorrelation FDT. The Markovian inhomogeneousclosures (MIC) are established from the quasi-diagonal direct interaction approximation (QDIA)theory by modifying the response function to aMarkovian form and employing the respective FDTvariants.In the MICs, Markov equations for the triad re-laxation functions are derived that carry similarinformation to the time-history integrals of thenon-Markovian QDIA closure. A further approxi-mation is applied whereby analytic forms for thetriad relaxation rates are formulated. The result-ing simple Markovian inhomogeneous closureis analagous to the eddy damped quasi-normal(EDQNM) approximation developed by Orszag(1970) for homogeneous isotropic turbulence. TheMICs are considerably more computationally effi-cient for long integrations as compared to the QDIAallowing, for the first time, investigation of inertialranges using inhomogeneous statistical dynamicalclosures.

Far from equilibrium processes are studied, includ-ing the impact of a westerly mean flow on a conicalmountain generating large-amplitude Rossby wavesin a turbulent environment, as well as observedtropospheric flows including atmospheric blockingphenomena. In general, excellent agreement isfound between the evolved mean streamfunctionand mean and transient kinetic energy spectra forthe three versions of the MIC and two variants of thenon-Markovian QDIA compared with an ensembleof 1800 direct numerical simulations (DNS).

3.5. Approximating Link Travel Time DistributionsSamithree Rajapaksha (Monash University)

16:00 Tue 3 December 2019 – 189

Mrs Samithree Rajapaksha, A/Prof. Tim Garoni and Dr

Lele Zhang

Investigating link travel time distributions is impor-tant for modelling vehicular dynamics in arterialroads. Most studies related to travel time distribu-tions are limited to empirical estimations. How-ever, results tend to be inconclusive. We proposed amodel based on Negative Binomial distributions toapproximate link travel time distributions and eval-uated its performance against a simple stochastictransport model, Asymmetric Simple Exclusion Pro-cess (ASEP).

3.6. Courier route optimization with unloadingbays information and reservation systemsLele (Joyce) Zhang (The University of Melbourne)

17:15 Tue 3 December 2019 – 189

Dr Lele (Joyce) Zhang

The demand for parcel deliveries in central city ar-eas has been growing fast as a result of rapid urban-ization and the development of e-commerce. Find-ing efficient routes for couriers undertaking deliver-ies in those areas is becoming more challenging dueto growing levels of congestion and difficulties in ac-cessing unloading bays. Developments in advancedon-line booking systems and sensor technologiesprovide great opportunities to improve delivery ef-ficiency and the utilization of unloading bays, andfurther to improve urban sustainability and livabil-ity. We developed a stochastic agent-based sim-ulation model to study the benefits of providingcouriers with unloading bay availability informa-tion and reservation opportunities, within which atwo-layer optimization model for the courier multi-modal routing problem. Numerical experimentswere conducted on a network similar to Melbourne’sCBD. It was found that when real-time average oc-cupancy or instantaneous availability information isprovided total delivery times are decreased due tosubstantial savings in driving arising from less circu-lation and searching for unoccupied unloading bays.Such a positive effect is more pronounced when noparking duration limits are applied, and lower driv-ing distances lead to better environmental perfor-mance. In addition, the unloading bay managementauthorities could coordinate the behavior of couri-ers via intelligently assigning reservations based ondelivery demand. In that case, the reservation sys-tem can guarantee the availability of unloading baysfor couriers so that uncertainty in undertaking deliv-eries can be greatly reduced and service quality andreliability can be enhanced. The coordination en-ables the delivery network to realize a system-wideoptimization, which can lead to approximately 38

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4. Category Theory

4.1. Characterising split opfibrations using lensesBryce Clarke (Macquarie University)

16:00 Wed 4 December 2019 – 188

Bryce Clarke

Split opfibrations are functors equipped with a suit-able choice of opcartesian lifts, and are perhaps bestknown as arising from Cat-valued functors underthe Grothendieck construction. When working in a2-category, split opfibrations may instead be definedas algebras for a particular 2-monad, however whenspecialising to Cat this is quite different from the or-dinary definition. In this talk, I will use lenses to in-troduce two alternative ways of defining split opfi-brations in Cat: the first utilising double categoriesand the second utilising the décalage of a category.I will explore how these definitions are linked andshow how they are generalised to the 2-category ofinternal categories.

4.2. The free tangent category on an affineconnectionRichard Garner (Macquarie University)

13:30 Wed 4 December 2019 – 188

Dr Richard Garner

A tangent category is a category C endowed withan endofunctor T : C → C which behaves like thetangent space functor on the category of smoothmanifolds. It provides an abstract setting for dif-ferential geometry, with instantiations including notonly the motivating example of smooth manifolds,but also categories of schemes, of deformation prob-lems, and of cocommutative coalgebras, as well asexamples coming from differential programming intheoretical computer science.

In a tangent category, there is a good notion of affineconnection on an object. In this talk, I will describejoint work with Geoff Cruttwell which describes thefree tangent category on an object with an affineconnection. The key idea is to encode the multi-linear calculus of (1,n)-tensor fields on such an ob-ject, which we do by way of a notion of “operadwith affine connection”. The punchline is that thefree tangent category on an affine connection is ex-actly the Lawvere theory generated by the free op-erad with affine connection.

4.3. t-structures and approximable triangulatedcategoriesBregje Pauwels (The University of Sydney)

16:25 Wed 4 December 2019 – 188

Dr Bregje Pauwels

Given a bounded-above cochain complex of mod-ules over a ring, it is standard to replace it by a pro-jective resolution, and it is classical that doing so canbe very useful.

Recently, Amnon Neeman introduced a modifiedversion of this idea in triangulated categories otherthan the derived category of a ring. A triangulatedcategory is approximable if this modified procedureis possible. The concept of approximability has ledto exciting new results, some of which I will discussin this talk. In particular, I will give sufficient con-ditions for when objects in a triangulated category Tgenerate the aisle of a t-structure on T.

4.4. Localising by spans and cospans, andfunctoriality of associated algebrasDavid Roberts (The University of Adelaide)

16:50 Wed 4 December 2019 – 188

Dr David Roberts

The 2-category of presentable stacks is a localisationof the 2-category of groupoids internal to the basesite at the trivial isofibrations (defined appropri-ately). It is equivalently the localisation of the sub-2-category of groupoids with complemented cofibra-tions as 1-morphisms at the trivial cofibrations, withmild extra assumptions on the base site. Both con-structions are special cases of an abstract construc-tion of a bicategory of fractions, with very little as-sumed about the site. This can be used when dis-cussing the functoriality of the ∗-algebra associatedto a groupoid, and, more generally the C∗-algebraassociated to more structured groupoids. This iswork in progress.

4.5. An embedding of the homotopy theory of2-categories into that of 2-complicial setsMartina Rovelli (The Australian National University)

15:35 Wed 4 December 2019 – 188

Viktoriya Ozornova and Martina Rovelli

It is desirable that a good candidate model for thehomotopy theory of (∞,n)-categories should inter-act nicely with the existent homotopy theory of strictn-categories. When n = 0,1, it is understood that thehomotopy theory of sets and of strict 1-categoriesembeds in that of ∞-categories and ∞-groupoids,essentially for all existing models. When n = 2and we consider 2-complicial sets as a model of(∞,2)-categories, the picture is more complicated.In this talk we will give an informal introduction to2-complicial sets and describe a homotopically fullyfaithful nerve construction that embeds the homo-topy theory of 2-categories in the (∞,2)-categoriesin the form of 2-complicial sets. This is joint workwith V. Ozornova.

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4.6. Graphical Sets and Mapping Class GroupsMichelle Strumila (The University of Melbourne)

14:20 Wed 4 December 2019 – 188

Ms Michelle Strumila

Infinity operads can be modelled by dendroidal setsvia the category of trees. When generalised to thecategory of graphs, one obtains a model for infinitymodular operads. One would hope, then, that in-finity modular operads satisfy some analogue of thenerve theorem; indeed, they do. Additionally, I havecreated a topological example of an infinity modularoperad. This involves mapping class groups of sur-faces, and in interesting because it comes at it fromthe graphical set perspective.

4.7. Regular Theories Enriched Over FinitaryVarietiesGiacomo Tendas (Macquarie University)

14:45 Wed 4 December 2019 – 188

Mr Giacomo Tendas

When talking about theories we may think of twodifferent approaches, a logical one and a categori-cal one. From the logical point of view, a theory isgiven by a list of axioms on a fixed set of operations,and its models are corresponding sets and functionsthat satisfy those axioms. For instance algebraic the-ories are those whose axioms consist of equationsbased on the operation symbols of the language (e.g.the axioms for abelian groups or rings). More gen-erally, if the axioms are still equations but the oper-ation symbols are not defined globally, but only onequationally defined subsets, we talk of essentiallyalgebraic theories. A further step can be made byconsidering regular theories, in which we allow ex-istential quantification over the usual equations.

Categorically speaking, we could think of a theory asa category C with some structure, and of a modelof C as a functor from C into Set which preservesthat structure; this approach was first introduced byLawvere. Algebraic theories then correspond to cat-egories with finite products, and models are finiteproduct preserving functors. On the other hand acategory with finite limits represents an essentiallyalgebraic theory, and functors preserving finite lim-its are its models. Regular theories correspond in-stead to regular categories: finitely complete oneswith coequalizers of kernel pairs, for which regularepimorphisms are pullback stable. Models here arefunctors preserving finite limits and regular epimor-phisms; we refer to them as regular functors.

These two notions, categorical and logical, can berecovered from each other: given a logical theory,there is a syntactic way to build a category with therelevant structure for which models of the theorycorrespond to functors to Set preserving this struc-ture, and vice versa.

In the context of regular theories, Barr showed thateach small and regular category C can be embedded

in a particular category of presheaves based on themodels of C; then in 1990 Makkai gave a simple ex-plicit characterization of the essential image of theembedding (in the case where the original regularcategory is moreover exact), giving a simple way torecover a theory from its models.

In this talk we define an enriched notion of reg-ularity, and prove a corresponding version of thetheorems of Barr and Makkai; all of this is doneenriching over finitary varieties: categories of theform FP(C,Set), consisting of finite product preserv-ing functors for some small category C with finiteproducts.

Joint work with Steve Lack

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5.1. Generation of random graphs with givendegreesAndrii Arman (Monash University)

15:10 Tue 3 December 2019 – G56

Dr Andrii Arman

In this talk I will discuss algorithms for a uniformgeneration of random graphs with a given degree se-quence. Let M be the sum of all degrees and ∆ bethe maximum degree of a given degree sequence.McKay and Wormald described a switching basedalgorithm for the generation of graphs with givendegrees that had expected runtime O(M 2∆2), underthe assumption ∆4 = O(M). I will present a modifi-cation of the McKay-Wormald algorithm that incor-porates a new rejection scheme and uses the sameswitching operation. A new algorithm has expectedrunning time linear in M , under the same assump-tions.

I will also describe how a new rejection schemecan be integrated into other graph generation algo-rithms to significantly reduce expected runtime, aswell as how it can be used to generate contingencytables with given marginals uniformly at random.

This talk is based on the joint work with Jane Gaoand Nick Wormald.

5.2. How generic ring algorithms and labelledbinary trees helped solve an outstanding factoringproblem in number theory.Lynn Batten (Deakin University)

13:55 Thu 5 December 2019 – G56

Prof Lynn Batten

We show how generic ring algorithms can be identi-fied with rooted partially labelled binary trees wherebranches in the tree correspond to equality queries,and non-branching vertices correspond in a natu-ral way to polynomials. We then describe how Ag-garwal and Maurer, in 2016, used this identifica-tion to prove the existence of a probabilistic polyno-mial time algorithm taking as input a product of twoprime numbers and factoring this with probabilitygreater than or equal to one half.

5.3. Universal Bijections for Positive AlgebraicStructuresRichard Brak (The University of Melbourne)

17:15 Tue 3 December 2019 – G56

Dr Richard Brak

Many well know combinatorial families (Catalan,Motzkin, Schroeder, Catalan-Fuss, ...) are exam-ples of positive algebraic structures (a certain con-dition on the algebraic equation the ordinary gen-erating satisfies). We will show that all such struc-tures can be given a generalised magma structure. If

the magma is free then the universal isomorphismbetween generalised magma of the same type de-fine a universal recursive size preserving bijectionbetween all such structures eg. a single bijection thatapplies to any pair of Catalan structures. We alsoprovide a combinatorial theorem that characterisesa generaised free magma.

5.4. The firebreak problemAndrea Burgess (University of New Brunswick)

14:20 Thu 5 December 2019 – G56

Kathleen Barnetson, Andrea Burgess, Jessica Enright,

Jared Howell, David Pike, Brady Ryan

Suppose a network is represented by a graph G . Afire (or some sort of contagion) breaks out at a ver-tex, and we may respond by establishing a firebreakby protecting k other vertices of G . The fire can-not burn or pass through these k protected vertices;however, the fire subsequently spreads to all verticesit can reach without passing through the firebreak.A natural question arises: how many vertices can wesave from being burned?

In this talk, we consider the corresponding de-cision problem. We show that this problem isintractable on split graphs and bipartite graphs,but polynomial-time solvable on several othergraph classes, such as cubic graphs and graphs withbounded treewidth.

5.5. Heffter Arrays with compatible and simpleorderingsNicholas Cavenagh (University of Waikato)

13:30 Wed 4 December 2019 – G56

Dr Nicholas Cavenagh

In the last 20 years biembedding pairs of designsand cycle systems onto surfaces has been a much-researched topic (see the 2007 survey “Designs andTopology” by Grannell and Griggs). In particular, ina posthumous work (2015), Archdeacon showed thatbiembeddings of cycle systems may be obtained viaHeffter arrays. Formally, a Heffter array H(m,n; s, t )is an m ×n array of integers such that:

• each row contains s filled cells and eachcolumn contains t filled cells;

• the elements in every row and column sumto 0 in Z2ms+1; and

• for each integer 1 ≤ x ≤ ms, either x or −xappears in the array.

If we can order the entries of each row and columnsatisyfing two properties (compatible and simple), aHeffter array yields an embedding of two cycle de-compositions of the complete graph K2ms+1 onto an

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orientable surface. Such an embedding is face 2-colourable, where the faces of one colour give a de-composition into s-cycles and the faces of the othercolour gives a decomposition into t-cycles. Thus as acorollary the two graph decompositions are orthog-onal; that is, any two cycles share at most one edge.Moreover, the action of addition in Z2ms+1 gives anautomorphism of the embedding. We give more de-tail about the above and present a new result: the ex-istence of Heffter arrays H(n,n; s, s) with compatibleand simple orderings whenever s ≡ 3 (mod 4) andn ≡ 1 (mod 4).

5.6. Properties of the polytope of polystochasticmatricesWilliam Crawford (Monash University)

17:15 Wed 4 December 2019 – G56

Mr William Crawford

A d-dimensional matrix is called 1-polystochastic if itis non-negative and the sum over each line equals 1.Such a matrix that has a single 1 in each line andzeros elsewhere is called a 1-permutation matrix. Adiagonal of a d-dimensional matrix of order n is achoice of n elements, no two in the same hyper-plane. The permanent of a d-dimensional matrix isthe sum over the diagonals of the product of the ele-ments within the diagonal.

For a given order n and dimension d , the set of1-polystochastic matrices forms a convex polytopethat includes the 1-permutation matrices within itsset of vertices. For even n and odd d , we give a con-struction for a class of 1-permutation matrices withzero permanent. Consequently, we show that the setof 1-polystochastic matrices with zero permanent

contains at least nn3/2(1/2−o(1)) 1-permutation matri-ces and contains a polytope of dimension at leastcn3/2 for fixed c,d and even n → ∞. We also pro-vide counterexamples to a conjecture by Taranenkoabout the location of local extrema of the perma-nent.

5.7. MaxMinSum Steiner Systems forAccess-Balancing in Distributed StorageSon Hoang Dau (RMIT University)

16:00 Fri 6 December 2019 – G56

Dr Son Hoang Dau

Many code families such as low-density parity-check codes, fractional repetition codes, batchcodes, and private information retrieval codes withlow storage overhead rely on the use of combina-torial block designs or derivatives thereof. In thecontext of distributed storage applications, oneis often faced with system design issues that im-pose additional constraints on the coding schemesand therefore on the underlying block designs.Here, we address one such problem, pertaining toserver access frequency balancing, by introducing anew form of Steiner systems, termed MaxMinSum

Steiner systems. MaxMinSum Steiner systems arecharacterized by the property that the minimumvalue of the sum of points (elements) within a blockis maximized or that the minimum sum of blockindices containing some fixed point is maximized.We show that proper relabelings of points in theBose and Skolem constructions for Steiner triplesystems lead to optimal MaxMin values for the sumsof interest; for the duals of the designs, we exhibitblock labelings that are within a 3/4 multiplicativefactor from the optimum.

5.8. On determining when small embeddings ofpartial Steiner triple systems existAjani De Vas Gunasekara (Monash University)

13:55 Wed 4 December 2019 – G56

Darryn Bryant, Ajani De Vas Gunasekara, Daniel Horsley

A partial Steiner triple system of order u is a pair(U ,A ) where U is a set of u vertices and A is a set oftriples of elements in U such that any two elementsof U occur together in at most one triple. If eachpair of elements occur together in exactly one tripleit is a Steiner triple system. An embedding of a partialSteiner triple system (U ,A ) is a (complete) Steinertriple system (V ,B) such that U ⊆V and A ⊆B. Fora given partial Steiner triple system of order u it isknown that an embedding of order v ≥ 2u +1 existswhenever v satisfies the obvious necessary condi-tions. Determining whether “small” embeddings oforder v < 2u+1 exist is a more difficult task. Here weextend a result of Colbourn on theNP-completenessof these problems.

5.9. Some problems suggested by the OnlineGraph Atlas projectGraham Farr (Monash University)

17:40 Wed 4 December 2019 – G56

Prof Graham Farr

The Online Graph Atlas (OLGA) is an electronicrepository of all graphs (up to isomorphism) upto some order (currently 10), together with valuesof several important parameters for each graph.It has been built at Monash University and wasoriginally inspired by the printed repository of Readand Wilson. The latest version has been built bySrinibas Swain in collaboration with Paul Bonning-ton, Graham Farr and Kerri Morgan. In this talk, wepresent some graph-theoretic questions raised bythis project.

One family of questions we consider is the following.Let f be a nonnegative integer-valued graph param-eter, invariant under isomorphism. We seek to cal-culate f recursively, using its values on subgraphsobtained by deleting single vertices or single edges.Sometimes — e.g., if f is circumference — this canbe done exactly, and this is useful as it helps us cal-culate the values of f efficiently for all graphs in the

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repository. At other times, we do not know of an ex-act recurrence, but it is often the case that we canstill find simple recursive upper and lower bounds.For example, in some situations — such as if f istree-width or degeneracy — we may be able to showthat, for all v ∈V (G),

max f (G−v) | v ∈V (G) ≤ f (G) ≤ 1+min f (G−v) | v ∈V (G).

For such an f , we are especially interested in howoften these bounds coincide, because in such caseswe know the value of f exactly. When the bounds donot coincide, we must resort to some other methodto compute f , and this may be costly.

Let the proportion of n-vertex graphs for which thebounds coincide be µ f (n). We ask:

(1) Do there exist constants L f > 0 and U f <1 such that L f ≤ µ f (n) ≤ U f for all suffi-ciently large n?

(2) Does limn→∞µ f (n) exist?

These questions may be asked for any f . We discusssome specific parameters and report some compu-tational results for them.

This is joint work with Srinibas Swain, Paul Bonning-ton and Kerri Morgan.

5.10. Learning Large Random Graphs Via GroupQueriesMatthias Fresacher (University of Adelaide)

16:25 Tue 3 December 2019 – G56

Mr Matthias Fresacher

This report examines algorithms that learn largerandom graphs via nonadaptive noiseless groupqueries. Specifically, it examines how to minimisethe number of testes required to fully learn a ran-dom graph. The analysis draws on techniques fromgroup testing and applies them in a random graphsetting.

In particular, the COMP algorithm is analysed anda theoretical upper bound on the number of testrequired established. A theoretically algorithm-independent lower bound is also examined toprovide a lower bound on the number of testsrequired to provide a comparison. Both of thesebounds hold for most scaling regimes of interest inregard to the number of edges and nodes containedin the random graph.

Further, the learning of random graphs is shown tobe solvable using ILP and LP techniques. These al-gorithms along with the DD algorithm are then com-pared in simulations in an attempt to empiricallyverify the theoretical results.

5.11. Perfect 1-factorisations of K16

Michael James Gill (Monash University)

16:50 Wed 4 December 2019 – G56

Mr Michael James Gill

A 1-factorisation of the complete graph K2n is per-fect if the union of each pair of 1-factors is a Hamil-tonian cycle. Dinitz and Garnick (1996) found 23perfect 1-factorisations of K14. Meszka and Rosa(2003) found 88 perfect 1-factorisations of K16 withnon-trivial automorphisms. Using partially orderedtraversal techniques and edge selection heuristics,we found all 3155 perfect 1-factorisations of K16

including 89 with non-trivial automorphisms. Weevaluated the efficacy of two well studied isomor-phism invariants and proposed two new isomor-phism invariants. We also proved the non-existenceof a symmetric atomic Latin square of order 15.

5.12. New bounds on the maximum size ofSperner partition systemsAdam Gowty (Monash University)

14:20 Wed 4 December 2019 – G56

Mr Adam Gowty

An (n,k)-Sperner partition system is a collection ofpartitions of an n-set into k nonempty classes, thatsatisfies the requirement that no class is a subset ofanother. In this talk, we shall discuss a constructionfor Sperner partitions systems that, as n

k grows large,produces systems for which the number of parti-tions they contain is asymptotic to the best possible.

5.13. Constructions of Difference Covering Arraysusing Skolem sequencesJoanne Hall (Royal Melbourne Institute of Technology)

15:10 Fri 6 December 2019 – G56

Joanne Hall and Asha Rao

Difference Covering Arrays (DCA) are a generalisa-tion of difference matrices, and provide a useful toolfor experimental designs. Difference covering arrayscan be used to construct mutually orthogonal Latinsquares, transversal coverings, and covering arrays,with applications in software testing, error correct-ing codes, and experimental design. We use Skolemsequences to construct new families of DCA, andclassify isomorphism classes of DCA.

5.14. Covering radius in the Hammingpermutation spaceKevin Hendrey (Institute for Basic Science)

16:25 Fri 6 December 2019 – G56

Kevin Hendrey, Ian M. Wanless

Our problem can be described in terms of a twoplayer game, played with the set Sn of permutationson 1,2, . . . ,n. First, Player 1 selects a subset S of Sn

and shows it to Player 2. Next, Player 2 selects a per-mutation p from Sn as different as possible from thepermutations in S, and shows it to Player 1. Finally,Player 1 selects a permutation q from S, and theycompare p and q . The aim of Player 1 is to ensurethat p and q differ in few positions, while keeping

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the size of S small. The function f (n, s) can be de-fined as the minimum size of a set S ⊆Sn that Player1 can select in order to gaurantee that p and q willdiffer in at most s positions.

I will present some recent results on the functionf (n, s). We are particularly interested in determin-ing the value f (n,2), which would resolve a conjec-ture of Kézdy and Snevily that implies several fa-mous conjectures for Latin squares. Here we im-prove the best known lower bound, showing thatf (n,2) Ê 3n/4. Joint work with Ian M. Wanless.

5.15. Generating digraphs with derangementsDaniel Horsley (Monash University)

14:45 Wed 4 December 2019 – G56

Daniel Horsley, Moharram Iradmusa, Cheryl E. Praeger

A collection S of derangements of a set V generatesa (possibly infinite) digraph with vertex set V and arcset (x,σ(x)) : x ∈V ,σ ∈S . Here we characterise, foreach positive integer k, the digraphs that can be gen-erated by at most k derangements. Our result resem-bles the De Bruijn-Erdos theorem in it characterisesa property of an infinite graph in terms of propertiesof its finite subgraphs.

5.16. Excluded minors for classes of binaryfunctionsBenjamin Jones (Monash University)

14:20 Tue 3 December 2019 – G56

Mr Benjamin Jones

The rank of a set of edges in a graph is the size ofthe largest forest contained in that set. It is wellknown that the deletion and contraction operationscan be expressed in terms a graph’s rank function,and the operations generalise to rank functions ofother combinatorial structures, including matroidsand polymatroids.

In (Farr, 1993), every rank function r : 2E → R is as-signed a binary function Q†r : 2E → R by the trans-form Q†, given by

Q†r (X ) := (−1)|X | ∑Y ⊆X

(−1)|Y |2r (E)−r (E\Y ).

When r is the rank function of a binary matroid,Q†r is the indicator function of its associated bi-nary vector space (cocircuit space). For graph rankfunctions, this is the space generated by the mini-mal edge cutsets. The deletion and contraction op-erations were extended to binary functions.

In this talk, we examine some minor-closed classesof rank functions using binary functions, and de-termine their excluded minors within the class ofbinary functions. These include the classes of bi-nary matroids, matroids and polymatroids. This ap-proach yields a new proof of Tutte’s excluded mi-nor characterisation of binary matroids, by lookingat their excluded minors in the more general class ofbinary functions.

5.17. An improved lower bound on Hong andLoewy’s numbersVesa Kaarnioja (University of New South Wales)

15:35 Fri 6 December 2019 – G56

Dr Vesa Kaarnioja

Let Kn be the set of all nonsingular n ×n lower tri-angular Boolean matrices. Hong and Loewy (2004)introduced the numbers

cn := minλ |λ is an eigenvalue of X X T, X ∈ Kn, n ∈Z+.

These numbers appear, e.g., in the estimation of thespectral radii of GCD and LCM matrices as well astheir lattice-theoretic counterparts.

In this talk, we present a new lower bound for thenumbers cn . This bound improves the previous es-timates derived by Mattila (2015) and Altınısık etal. (2016). The sharpness of this lower bound isassessed numerically, which leads us to conjecturethat cn ∼ 5ϕ−2n as n →∞.

5.18. A curious bijection between Dyck pathsKevin Limanta (University of New South Wales)

17:40 Tue 3 December 2019 – G56

Mr Kevin Limanta

Given a two-dimensional integer lattice Z2, one canconstruct a lattice path starting at (0,0) which con-sists of up-steps (1,1) and down-steps (1,−1). ADyck path of semi-length n (or of length 2n) is sucha lattice path between (0,0) and (2n,0) which nevergoes below the x-axis. It is well-known that the num-ber of all Dyck paths of semi-length n is the nthCatalan number given by the sequence A000108 inOEIS. In this talk, I will describe an interesting bijec-tion between the set of Dyck paths of semi-length nwhich was motivated by a bijection given by Elizaldeand Deutsch.

5.19. On the Cyclic Matching sequenceablility ofregular graphsAdam Mammoliti (Monash University)

16:25 Wed 4 December 2019 – G56

Daniel Horsley, Adam Mammoliti

The cyclic matching sequenceability of a graph G isthe largest integer s such that there exists a sequenceof the edges of G so that every s cyclically consec-utive edges form a matching. The cyclic matchingsequenceability is known for several special typesof graphs but little is known in general about largeclasses of graphs.

In this talk I will present several results concerningcyclic matching sequenceability of general graphsand more specialised results for regular graphs. Inparticular, I will present upper and lower boundsof the cyclic matching sequenceability of generalgraphs. Finally, I will present results on the min-imum cyclic matching sequenceability of 2-regular

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graphs and lower and upper bounds on the mini-mum cyclic matching sequenceability of k-regulargraphs for k ≥ 3. This is joint work with Daniel Hors-ley

5.20. The Cheeger constant for distance-regulargraphs.Greg Markowsky (Monash University)

13:55 Fri 6 December 2019 – G56

Dr Greg Markowsky

The Cheeger constant of a graph is the smallestpossible ratio between the size of a subgraph andthe size of its boundary. It is well known that thisconstant must be at least λ1/2 , where λ1 is thesmallest positive eigenvalue of the Laplacian ma-trix. In this talk I will discuss the conjecture that fordistance-regular graphs the Cheeger constant is atmost λ1. The conjecture has been proved for mostof the known infinite families of distance-regulargraphs, for distance-regular graphs of diameter 2(the strongly regular graphs), for several classes ofdistance-regular graphs of diameter 3, and for mostdistance-regular graphs with small valency. A num-ber of cases remain open. Joint work with JacobusKoolen and Zhi Qiao.

5.21. Geometric hypergraph colouring problemsMichael Payne (La Trobe University)

16:00 Wed 4 December 2019 – G56

Dr Michael Payne

Given a set of points in the plane, and a familyof shapes, one can define a k-uniform hypergraphwhose hyperedges are sets of k points contained inone of the shapes. This general procedure gives riseto a wide variety of interesting classes of hypergraph,including well studied graph classes such as planargraphs and Delaunay triangulations.

In this talk we will discuss colouring problems re-lated to some such hypergraph classes, with a par-ticular focus on hypergraphs with poset dimensionat most three. In the right light, these can be seen asa natural generalisation of planar graphs.

5.22. Minkowski decompositions of polytopes viageometric graphsGuillermo Pineda-Villavicencio (Deakin University)

15:35 Wed 4 December 2019 – G56

Dr Guillermo Pineda-Villavicencio

Minkowski decomposition of polytopes is presentedvia geometric graphs. This is due to Kallay (1982),who reduced the decomposability of a realisation ofpolytope to that of its geometric graph, and in thisway, introduced the decomposability of geometricgraphs. One advantage of this approach is its ver-satility. The decomposability of polytopes reducesto the decomposability of geometric graphs, whichare not necessarily polytopal. And statements on

decomposability of geometric graphs often revolvearound the existence of suitable subgraphs or usefulproperties in the graphs.

As applications, we revisit many of the known re-sults in this area, including the classifications intodecomposable and decomposable, of d-polytopeswith at most 2d vertices due to Kallay (1979), andof d-polytopes with 2d+1 vertices due to Pineda-Villacicencio et al (2018). We will also present a3-polytope with both a decomposable realisationand an indecomposable realisation, showing in thestrongest possible way that decomposability is not acombinatorial property.

The talk concludes with the main open problems inthe area.

5.23. Middle Product Learning With ErrorsAmin Sakzad (Monash University)

13:30 Thu 5 December 2019 – G56

Dr Amin Sakzad

We introduce a new variant MP-LWE of the LearningWith Errors problem (LWE) making use of the Mid-dle Product between polynomials modulo an inte-ger q . We exhibit a reduction from the Polynomial-LWE problem (PLWE) parametrized by a polynomialf , to MP-LWE which is defined independently of anysuch f . The reduction only requires f to be monicwith constant coefficient coprime with q . It incursa noise growth proportional to the so-called expan-sion factor of f . We also describe a public-key en-cryption scheme with quasi-optimal asymptotic ef-ficiency (the bit-sizes of the keys and the run-timesof all involved algorithms are quasi-linear in the se-curity parameter), which is secure against chosenplaintext attacks under the MP-LWE hardness as-sumption. The scheme is hence secure under theassumption that PLWE is hard for at least one poly-nomial f of degree n among a family of f ’s which isexponential in n.

5.24. Counting automorphisms of random treeswith martingalesAngus Southwell (Monash University)

16:50 Tue 3 December 2019 – G56

Mr Angus Southwell

Yu (Automorphisms of random trees, PhD thesis,2012) conjectured that the distribution of the num-ber of automorphisms of a random labelled tree isasymptotically lognormal. We prove this conjec-ture using a new general martingale approach forproperties of random labelled trees. To apply ourtheory, we show that the logarithm of the numberof automorphisms is stable with respect to smallperturbations. In this talk I give the central limittheorem for general tree parameters and thendemonstrate how to apply it to this problem.

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5.25. Some examples of nonnormal Cayley graphson nonabelian simple groupsBinzhou Xia (The University of Melbourne)

14:20 Fri 6 December 2019 – G56

Dr Binzhou Xia

A Cayley graph on a group G is said to be nonnor-mal if the right multiplication action of G on itselfinduces a non-normal subgroup of the full automor-phism group of the Cayley graph. Nonnormal Cayleygraphs are believed to be rare among all the Cayleygraphs. In this talk, I will present some infinite fami-lies of nonnormal Cayley graphs on nonabelian sim-ple groups, whose existence was asked in the litera-ture.

5.26. Bounded Difference Inequalities forGraph-Dependent Random VariablesRui Zhang (Monash University)

16:00 Tue 3 December 2019 – G56

Mr Rui Zhang

We establish exponential concentration bounds forLipschitz functions of dependent random variables,whose dependencies are specified by dependencygraphs. The proof is based on Cramér-Chernoffmethod using martingales and coupling. These areextensions of McDiarmid’s bounded difference in-equality to the dependent cases. We also provideapplications and examples in statistics and machinelearning.

5.27. The vertex-isoperimetric number of theincidence graphs of unitals and finite projectivespacesSanming Zhou (The University of Melbourne)

13:30 Fri 6 December 2019 – G56

Prof Sanming Zhou

A fundamental problem in graph theory is to un-derstand various expansion properties of graphs.The expansion of a graph is commonly measuredby its isoperimetric number (also known as Cheegerconstant) or its vertex-isoperimetric number. Iwill talk about some recent results on the vertex-isoperimetric number of the incidence graph ofunitals and the point-hyperplane incidence graphof PG(n, q), where a unital is a 2-(n3 + 1,n + 1,1)design for some integer n ≥ 2.

Joint work with Andrew Elvey-Price, Alice M. W. Huiand Muhammad Adib Surani.

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6. Computational Mathematics

6.1. Bragg Edge Neutron Transmission StrainTomography using the Finite Element MethodRiya Aggarwal (The University of Newcastle)

16:50 Wed 4 December 2019 – 189

Ms Riya Aggarwal

Bragg edge strain imaging from energy-resolvedneutron transmission measurements poses an in-teresting tomography problem. The solution to thisproblem will allow the reconstruction of detailedstress and strain distributions within polycrystallinesolids from sets of Bragg edge strain images. In theproposed method, we provide a general approachto reconstruction of an arbitrary system basedon a finite element approach with least-squaresprocess constrained by equilibrium. This approachhas developed in two dimensions before beingdemonstrated experimentally on the samples usingthe RADEN instrument at the J-PARC spallationneutron source in Japan. Validation of the resultingreconstructions has provided through a comparisonto conventional constant wavelength strain mea-surements carried out on the KOWARI engineeringdiffractometer within ANSTO in Australia.

6.2. Uncertainty Quantification for the LinearElastic equationsMichael Clarke (UNSW Sydney)

16:00 Wed 4 December 2019 – 189

Mr Michael Clarke

The notion of assigning random fields to parametersin PDE’s in order to compute a quantity of interest,namely a functional of the solution, has been in-vestigated rigorously for uniform distributions andsubsequently the log-normal case. The body of workthus far has considered elliptic PDE’s of the sametype as the diffusion equation and a generalisationto affine parametric operator equations, both ofwhich were restricted to one random field input.We have sought to extend these methodologiesto Navier’s equations of linear elasticity whichcontain two elastic moduli (Lamé parameters) asrandom field expansions. The computation of anexpectation value of the solution is approachedusing a Quasi-Monte Carlo (QMC) quadrature rule,

motivated by the higher order convergence O(N− 1p )

achieved for deterministic interlaced polynomiallattice point sets, where p is a smoothness pa-rameter related to the integrand function, and thecomputational cost is reduced by using a SparseGrid truncation. We provide a priori estimates andregularity results in the natural Sobolev space set-ting, accounting for each source of numerical error,and we compare the numerical results with these

theoretical estimates. Furthermore we outline on-going work, informed by the Multi-Level QMC rule,whereby the aim is to minimise the computationalcost required to achieve a fixed error bound and,in doing so, we treat each discretisation parameterfor the numerical problem as an index set on anextended Sparse Grid.

This work has been undertaken jointly with JosefDick, Quoc Thong Le Gia and Bishnu Lamichhane.

6.3. High-order numerical schemes for degenerateelliptic equationsJerome Droniou (Monash University)

13:55 Thu 5 December 2019 – 189

A/Prof. Jerome Droniou, Prof. Robert Eymard

The Stefan equation is a well-known degenerate par-abolic equation that models the evolution of a mate-rial that transitions from one phase to another. It iswritten

∂t u −∆ζ(u) = f

(with appropriate initial and boundary conditions),where ζ : R → R is non-decreasing but can haveplateaux. Here, u represents the energy of the ma-terial and ζ(u) its temperature, and the plateaux of ζrepresents the well-known situation where the ma-terial receives energy that enables a phase transi-tion without increase of temperature (think of boil-ing water, which remains at 100 degrees while it isboiling).

When using an implicit time-stepping scheme (e.g.Euler or, more generally, discontinuous Galerkin intime), one ends up having to discretise in space thefollowing stationnary version of this model:

(?) u −∆ζ(u) = f .

Because of the plateaux of ζ, this equation is a de-generate elliptic equation, which looses its ellipticitywhen u reaches values corresponding to a plateauof ζ. Due to this change of nature, designing sta-ble numerical schemes for (?) is tricky, even moreso when one seeks very accurate approximations –namely, high-order numerical methods.

In this talk, after briefly highlighting the main prin-ciples for finding a stable scheme for (?), we willexplain how high-order numerical approximationsof this equation can be designed. The stability re-lies on a proper notion of mass-lumping, which usespiecewise constant approximations. This choiceseems in first instance incompatible with a high-order approximation, but we will identify conditionson the cell-wise quadrature rules that ensure an el-evated accuracy of the scheme. Appropriate quad-rature rules can be designed in 1D and on triangularmeshes in 2D, and we will present various numerical

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results obtained by Pk finite elements and discontin-uous galerkin methods.

6.4. Unfitted Nitsche’s method for computing edgemodes in photonic grapheneHailong Guo (The University of Melbourne)

14:45 Wed 4 December 2019 – 189

Dr Hailong Guo

Photonic graphene, a photonic crystal with hon-eycomb structures, has been intensively studiedin both theoretical and applied fields. Similar tographene which admits Dirac Fermions and topo-logical edge states, photonic graphene supportsnovel and subtle propagat- ing modes (edge modes)of electromagnetic waves. These modes have wideapplications in many optical systems. In this paper,we propose a new unfitted Nitsche’s method tocomputing edge modes in photonic graphene withsome defect. The unique feather of the methods isthat it can arbitrary handle high contrast with geo-metric unfitted meshes. We establish the optimalconvergence of methods. Numerical examples arepresented to validate the theoretical results and tonumerically verify the existence of the edge modes.

6.5. Approximating functions of the precisionmatrix of Gaussian processesMarkus Hegland (Australian National University)

13:30 Wed 4 December 2019 – 189

Prof Markus Hegland

We are considering the approximation of functionsof covariance or precision matrices of Gaussian pro-cesses. We are working on a new approach whichuses Chebyshev polynomials and a Moebius trans-form which maps the spectrum of the precision ma-trix onto the interval (0,1). We have implementedthe approach and will report on some tests for ma-trices from a paper by Pettit, Weir and Hart. We usePython, Chebfun and spatial indexing based on a kd-tree from Scipy’s spatial algorithms and data struc-tures package to generate large and sparse precisionmatrices.

This is joint work with Prof. Ian Turner, QUT.

6.6. Probabilistic Saturations and Alt’s Problem inMechanism DesignMartin Helmer (Australian National University)

18:05 Wed 4 December 2019 – 189

Dr Martin Helmer

Alt’s problem formulated in 1923 is to count thenumber of four-bar linkages whose coupler curveinterpolates nine general points in the plane. Thisproblem can be formulated as counting the num-ber of solutions to a system of polynomial equationswhich was first solved numerically using homotopycontinuation by Wampler, Morgan, and Sommese in1992.

Since there is still not a proof that all solutions wereobtained, we consider upper bounds for Alt’s prob-lem by counting the number of solutions outsideof the base locus to a system arising as the generallinear combination of polynomials. In particular,we derive effective symbolic and numeric methodsfor studying such systems using probabilistic satu-rations that can be employed using both finite fieldsand floating-point computations.

The methods are probabilistic and we give boundson the size of finite field required to achieve a de-sired level of certainty. Both theoretical and compu-tational results and methods will be discussed.

This talk is based on joint work with JonathanHauenstein (University of Notre Dame).

6.7. Parallel time integration of hyperbolic PDEsOliver krzysik (Monash University)

15:35 Wed 4 December 2019 – 189

Mr Oliver krzysik

Parallel-in-time methods, such as multigridreduction-in-time (MGRIT) and Parareal, pro-vide an attractive option for increasing concurrencywhen simulating time-dependent PDEs in mod-ern high-performance computing environments.While these techniques have been very successfulfor diffusion-dominated equations, it has oftenbeen observed that their performance suffers dra-matically when applied to advection-dominatedproblems or purely hyperbolic PDEs. In this talk, Iwill give a brief introduction to these algorithms andshow examples of the aforementioned behaviour.I show that this degradation can be understoodfrom existing convergence theory of these solvers,and I consider designing their components thoughapproximately maximising convergence-rate esti-mates. Finally, for the canonical hyperbolic PDE ofconstant-coefficient linear advection, I show for thefirst time that fast and scalable parallel time inte-gration is possible, achieving convergence in just ahandful of iterations, even for high-order-accuratediscretizations.

6.8. A multiscale radial basis function method forseverely ill-posed problems on spheresQuoc Thong Le Gia (University of New South Wales)

14:20 Thu 5 December 2019 – 189

Dr Quoc Thong Le Gia

We propose and analyse the support vector ap-proach to approximating the solution of a severelyill-posed problem Au = f on the sphere, in which Ais an ill-posed map from the unit sphere to a concen-tric larger sphere. The Vapnik’s ε-intensive functionis adopted in the regularisation technique to reducethe error induced by noisy data. The method is thenextended to a multiscale algorithm by varying thesupport radius of the radial basis functions at eachscale. We discuss the convergence of the multiscale

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support vector approach and provide strategies forchoosing both regularisation parameters and cut-offparameters at each level. Numerical examples areconstructed to verify the efficiency of the multiscalesupport vector approach.

This is a joint work with Ian Sloan (UNSW) and MinZhong (Southeast University, China).

6.9. The Virtual Element Method for solvingpartial differential equations on unstructuredpolytopal meshesGianmarco Manzini (Consiglio Nazionale delle

Ricerche (CNR) - Italy)

13:55 Wed 4 December 2019 – 189

Dr Gianmarco Manzini

In this talk, we first review some ideas concern-ing numerical methods for solving Partial Differen-tial Equations (PDEs) of elliptic and parabolic typeon a computational domain that is partitioned byunstructured meshes admitting elements with verygeneral geometric shapes. Then, we present the Vir-tual Element Method (VEM), which is a very specialkind of Finite Element Method (FEM) that does notrequire explicit knowledge of the basis functions inthe discretization. In fact, the VEM makes system-atic use of projections onto polynomials subspacesin the construction of the discrete bilinear formsused in the weak formulations. A suitable choiceof the degrees of freedom allows these polynomialprojections to be computable even if the projectedfunction is unknown. The VEM has different for-mulations as the FEM (conforming, nonconforming,mixed, etc), and the fact that basis functions mustnot be explicitly computed makes the method ex-tremely flexible in applications. We terminate thetalk by showing numerical results to illustrate the ac-curacy and the robustness of the method.

6.10. Pressure Buildup in Surtseyan EjectaMark Joseph McGuinness (Victoria University of

Wellington)

17:15 Wed 4 December 2019 – 189

Mark McGuinness, Emma Greenbank

A Surtseyan eruption is a particular kind of vol-canic eruption which involves the bulk interactionof water and hot magma, mediated by the returnof ejected ash. Surtsey Island, off the coast of Ice-land, was born during such an eruption process inthe 1940s. Mount Ruapehu in New Zealand has alsofeatured Surtseyan eruptions, due to its crater lake.

One feature of such eruptions is ejected lava bombs,trailing steam, with evidence that watery slurry wastrapped inside them during the ejection process.Simple calculations indicate that the pressures de-veloped inside such a bomb should shatter it. Yet in-tact bombs are routinely discovered in debris piles.In an attempt to crack this problem, I will talk abouta transient mathematical model of the flashing of

water to steam inside one of these hot erupted lavaballs, with a particular focus on the maximum pres-sure developed and how it depends on the magmaproperties.

6.11. A stable finite volume scheme for nonlineardiffusion equations on general 2D meshesEl Houssaine QUENJEL (Nice Sophia Antipolis

University)

16:25 Wed 4 December 2019 – 189

Dr El Houssaine QUENJEL

Diffusion problems arise in many complex applica-tions such as geothermal systems, soil remediationand chemotaxis models. The discretization of dif-fusion terms thanks to stable and consistent finitevolume methods on distorted grids is a challengingtask. In my talk I will present a simple idea on how tobuild such a finite volume scheme that preserves thephysics of the problem at the discrete level, namelythe positivity of the approximate solution and thedecay of the free energy for large times. These prop-erties are rigorously proved in the framework of thediscrete duality finite volume methods. Numericaltests are given to illustrate the ability of the proposedapproach to deal with sever meshes while keepingits efficiency and robustness.

6.12. An approach to electrical impedancetomography in unknown domainsJanosch Rieger (Monash University)

17:40 Wed 4 December 2019 – 189

Prof Bastian Harrach, Dr Janosch Rieger

Elliptical impedance tomography is a non-invasiveimaging technology. In contrast to computerisedtomography, it is not based on x-ray pictures, buton measurements of the electrical potential ofthe imaged body. The reconstruction of the con-ductivity inside the body, and hence its internalstructure, from boundary measurements is a non-linear ill-posed problem, and hence challengingfrom a computational perspective, even when theexact shape of the body is known. We propose anew method for the local reconstruction of con-ductivity anomalies from boundary measurementsthat seems to work even for bodies with completelyunknown geometry. The price we pay is that wecompute an approximation of the so-called convexsource support of the measurement instead of theactual anomaly.

6.13. A posteriori error estimation for nonlinearelliptic equationsThanh Tran (University of New South Wales)

13:30 Thu 5 December 2019 – 189

Thanh Tran

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We propose an a posteriori error estimation tech-nique for the finite element solution of the steady-state nonlinear reaction-diffusion equation on arectangular domain in two dimensions. Our a poste-riori error estimation scheme is an implicit methodand is based on the element residual method. Errorestimates are computed locally on each element asthe solution of a 2×2 linear system, which is simpleand cheap to solve. We prove that the proposederror estimates are asymptotically correct.

This is a joint work with Kenny Lau.

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7. Dynamical Systems and Ergodic Theory

7.1. Conformal and Invariant Measures forRandom Covering Weighted SystemsJason Atnip (University of New South Wales)

16:50 Wed 4 December 2019 – 123

Jason Atnip

We consider random, countable branch piecewisemonotonic maps of the interval. We show the exis-tence of unique conformal and invariant measuresunder the assumptions of random covering and acontracting potential. We also show that the systemis exponentially mixing with respect to the invariantmeasure. This is all accomplished via random conetechniques and transfer operator methods.

7.2. On the number of ergodic absolutelycontinuous invariant measures for higherdimensional random dynamical systemsFawwaz Batayneh (University of Queensland)

17:15 Wed 4 December 2019 – 123

Mr Fawwaz Batayneh

An admissible random Jablonski map is a non au-tonomous dynamical system such that at each timeω, the dynamical system is described by a PiecewiseC 2 and monotonic Jablonski map fω chosen froma collection f = fω : I N ω∈Ω which satisfies anon average expanding condition. At each time ω,the way of selecting the map fω comes from the socalled base map σ defined on a probability space(Ω,F ,P) which is assumed to be invertible, ergodicand P−preserving map.

The concept of sample measures in the random caseis the natural generalization of the notion of invari-ant measure in the case of deterministic dynami-cal systems. Sample measures for random compo-sitions of expanding interval maps have previouslybeen studied by Pelikan, Morita and in a more gen-eral setting by Buzzi. The author considered randomcompositions of Lasota-Yorke maps and proved thatthe associated skew product transformation admitsa finite number of ergodic absolutely continuous in-variant measures and provided an upper bound thatcontrols the number of these measures.

In the setting of a random compositions of Jablon-ski maps, we have proved that admissible randomJablonski maps are quasi compact and their associ-ated skew product admits a finite number of ergodicrandom absolutely continuous invariant measures.This talk will focus on providing upper bounds forthis number.

7.3. A spectral approach for quenched limittheorems for random dynamical systemsGary Froyland (University of New South Wales)

16:25 Wed 4 December 2019 – 123

Prof Gary Froyland

After a gentle introduction to statistical limit laws,I will discuss quenched (i.e. “realisation-wise”) ver-sions of (i) a large deviations principle, (ii) a centrallimit theorem, and (iii) a local central limit theoremfor non-autonomous dynamical systems. A key ad-vance is the extension of the spectral method, com-monly used in limit laws for deterministic maps, tothe general random setting. We achieve this via mul-tiplicative ergodic theory and the development of ageneral framework to control the regularity of Lya-punov exponents of twisted transfer operator cocy-cles with respect to a twist parameter. An impor-tant aspect of our results is that we only assume er-godicity and invertibility of the random driving; inparticular no expansivity or mixing properties arerequired. This is joint work with D. Dragicevic, C.González-Tokman, and S. Vaienti.

7.4. On the Dynamics of Inverse Magnetic BilliardsSean Gasiorek (The University of Sydney)

14:20 Thu 5 December 2019 – 123

Dr Sean Gasiorek

Consider a strictly convex set Ω in the plane, anda homogeneous, stationary magnetic field orthog-onal to the plane whose strength is B on the com-plement of Ω and 0 inside Ω. The trajectories of acharged particle in this setting are straight lines con-catenated with circular arcs of Larmor radius µ. Weexamine the dynamics of such a particle and call thisinverse magnetic billiards. Comparisons are madeto standard Birkhoff billiards and magnetic billiards,as some theorems regarding inverse magnetic bil-liards are consistent with each of these billiard vari-ants while others are not.

7.5. Characterization and perturbations of theLyapunov spectrum of a class of Perron-Frobeniusoperator cocyclesCecilia Gonzalez-Tokman (The University of

Queensland)

17:40 Wed 4 December 2019 – 123

Dr Cecilia Gonzalez-Tokman

The Lyapunov spectrum of Perron-Frobenius oper-ator cocycles contains relevant information aboutdynamical properties of time-dependent (non-autonomous, random) dynamical systems. In thistalk we characterize the Lyapunov spectrum of aclass of analytic expanding maps of the circle, anddiscuss stability and instability properties of this

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spectrum under perturbations. (Joint work withAnthony Quas.)

7.6. Multiscale modelling enables prediction andsimulation of floods and tsunamisDivahar Jayaraman (The University of Adelaide)

13:55 Wed 4 December 2019 – 123

J. Divahar

Floods and tsunamis are challenging to predict.Prediction (is a tsunami/flood on its way?) andsimulation (which areas would be affected?) wouldsave lives and assets. We primarily need to simulatewater height and velocity variations over many kilo-metres (macroscale characteristics), but the causeand manifestation of such kilometre-scale effectshappen at the sub-metre-scale (microscale). Hencewe cannot neglect the complex sub-metre-scalephysics, at the same time detailed simulation overmany kilometres is impractical. Our research aimsto accurately model the macroscale characteristicsof such complex waves by a detailed microscalesimulation only in a small fraction (about 0.01%)of the whole space. Patch dynamics multi-scalemethod performs detailed microscale simulationswithin small patches across the whole space andcouples the patches by interpolating their bound-ary values in macroscale. We are developing fewclasses of multi-scale methods (patch sche mes)generalising patch dynamics to accurately modelcomplex waves over large space. For representativesimple nonlinear waves with linear drag and viscousdiffusion, we find that the large waves in the patchscheme simulation match exactly (within numericalround-off errors) with the detailed microscale simu-lation over whole space. This assures that the patchschemes from the simulation over a small fractionof the whole space, successfully capture exactly,the corresponding macroscale characteristics in thetime evolution of waves. Thus, the developing patchschemes capture macroscale wave physics as accu-rately as the detailed microscale simulation, withlarge computational savings by several thousandtimes. Currently we are extending to more complexnonlinear viscous waves. Next we will extend toinclude turbulence which will enable accuratesimulation of real world floods and tsunamis overlarge space.

7.7. Blowing-up essential singularities in singularlyperturbed problemsSam Jelbart (The University of Sydney)

14:45 Wed 4 December 2019 – 123

Mr Sam Jelbart

Many dynamical systems feature essential singular-ities due to terms of the form e−h(x)/ε, ε → 0. Thepresence of such terms leads naturally to qualita-tively distinct dynamics depending on the sign ofh(x), and consequently to the presence of sharp

transitionary regions near h(x) = 0 when 0 < ε¿ 1.Problems with sharp transitions are frequently un-derstood using a combination of (geometric) singu-lar perturbation theory and geometric desingulari-sation (‘blow-up’) techniques. The usual methods,however, are not directly applicable to essential sin-gularities.

In this talk, we consider a model of transistor oscil-lations featuring an essential singularity of the kinddescribed above. In the context of this problem, wedescribe an extension for the traditional methods forgeometric desingularisation which make the analy-sis possible, allowing for a geometric proof of the ex-istence and uniqueness of the oscillations. Via thisanalysis, we hope to make the case that the methodsadopted have a more general applicability.

7.8. On Sil’nikov saddle-focus homoclinic orbitsKenneth James Palmer (National Taiwan University)

13:30 Thu 5 December 2019 – 123

Prof Kenneth James Palmer

Sil’nikov showed that that there is chaos in theneighbourhood of a saddle focus homoclinic or-bit.This talk reviews joint work of the speaker withFlaviano Battelli, Brian Coomes and Huseyin Koçakon these orbits. First an example due to Rodriguesof such an orbit in three dimensions is reviewed.This example is found by perturbing a system whichis degenerate in some sense. Other examples inthree dimensions have been found from numericalsimulations. It is shown how rigorous numericscan be used to prove that these examples are valid.Sil’nikov originally considered these orbits in 3dimensions but later he extended his theory tohigher dimensions. For these orbits it is necessaryto verify three further conditions. Originally theseconditions were geometric in nature but they are infact equivalent to conditions on bounded solutionsof the variational equation along the homoclinicorbit. These conditions are more easily verifiableand are used to construct of an orbit in 4 dimensionsby again perturbing a degenerate system. A rigorousnumerical method is also given for verifying that ahomoclinic orbit (in higher dimensions) found bynumerical simulations does in fact exist and satisfiesall of Sil’nikov’s conditions.

7.9. Application of local attractor dimension toreduced space strongly coupled data assimilationfor chaotic multiscale systemsCourtney Rose Quinn (CSIRO)

14:20 Wed 4 December 2019 – 123

Dr Courtney Rose Quinn

The basis and challenge of strongly coupled dataassimilation (CDA) is the accurate representationof cross-domain covariances between various cou-pled subsystems with disparate spatio-temporalscales, where often one or more subsystems are

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unobserved. In this study, we explore strong CDAusing ensemble Kalman filtering methods appliedto a conceptual multiscale chaotic model consistingof three coupled Lorenz attractors. We introducethe use of the local attractor dimension (i.e. theKaplan-Yorke dimension, dimK Y ) to determine therank of the background covariance matrix whichwe construct using a variable number of weightedcovariant Lyapunov vectors (CLVs). Specifically,we consider the ability to track the nonlinear tra-jectory of each of the subsystems with differentvariants of sparse observations, relying only onthe cross-domain covariance to determine an ac-curate analysis for tracking the trajectory of theunobserved subdomain. We find that spanningthe global unstable and neutral subspaces is notsufficient at times where the nonlinear dynamicsand intermittent linear error growth along a stabledirection combine. At such times a subset of the lo-cal stable subspace is also needed to be representedin the ensemble. In this regard the local dimK Y

provides an accurate estimate of the required rank.Additionally, we show that spanning the full spacedoes not improve performance significantly relativeto spanning only the subspace determined by thelocal dimension. Where weak coupling betweensubsystems leads to covariance collapse in one ormore of the unobserved subsystems, we apply anovel modified Kalman gain where the backgroundcovariances are scaled by their Frobenius norm.This modified gain increases the magnitude of theinnovations and the effective dimension of theunobserved domains relative to the strength of thecoupling and time-scale separation. We concludewith a discussion on the implications for higherdimensional systems.

7.10. A geometric proof of Ratner’s mixing ratesfor the horocycle flowDavide Ravotti (Monash University)

13:55 Thu 5 December 2019 – 123

Dr Davide Ravotti

For several parabolic systems, a technique oftenused to prove mixing and other strong chaotic prop-erties consists of a geometric shearing argument.In the case of the horocycle flow (both in constantand in variable negative curvature, as well as forits time-changes), this has been done successfullyby analysing the action of the horocycle flow ongeodesic arcs. The quantitative estimates one canobtain following this approach, however, are not op-timal, since, in the constant curvature case, do notmatch the ones obtained by Ratner. We will provean effective equidistribution result for the horocyclepush-forward of homogeneous arcs transverse tothe weak-stable leaves of the geodesic flow. As acorollary, we derive a geometric proof of Ratner’squantitative mixing result for the horocycle flow.

7.11. An empirical stability analysis of restrictedFour-Body modelAnoop Sivasankaran (Khalifa University of Science,

Technology)

13:30 Wed 4 December 2019 – 123

Dr Anoop Sivasankaran

Recently we have developed a global regularizationscheme that consists of adapted versions of sev-eral known regularisation transformations which re-moves all the singularities due to colliding pairs ofmasses. An algebraic optimisation algorithm is alsodeveloped for numerically implementing the reg-ularisation scheme which make use of the reversemode algorithmic differentiation. We use this newdeveloped method to empirically analyse the stabil-ity of a symmetrically restricted four body problemby studying the hierarchical evolution of a compre-hensive set of orbits appearing in the phase space.

7.12. Model reduction for the collective dynamicsof networks of coupled oscillatorsLachlan Smith (The University of Sydney)

16:00 Wed 4 December 2019 – 123

Dr Lachlan Smith

Many natural phenomena and industry applicationscan be modelled as networks of coupled oscilla-tors, including firefly flashing, neuron firing, andpower grid dynamics. A common phenomenon innetworks of coupled oscillators is synchronisation.Model reduction techniques aim to understand andquantify this low-dimensional emergent macro-scopic dynamics. In this talk I will present thecollective coordinate approach to model reductionfor networks of coupled oscillators, and comparethe collective coordinate approach with the widelyused Ott-Antonsen approach. I will show that thecollective coordinate approach yields a more accu-rate approximation for the macroscopic dynamicsof finite networks of coupled oscillators than theOtt-Antonsen approach, and recovers well-knownresults in the thermodynamic limit of infinitelymany oscillators.

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8. Financial mathematics

8.1. Modelling additional information: filtrationenlarged via a marked random timeAnna Aksamit (The University of Sydney)

13:55 Thu 5 December 2019 – 182

Dr Anna Aksamit

We consider enlargement of a reference filtrationthrough the observation of a random time and amark. Random time considered is such that its graphis included in the countable union of graphs of stop-ping times. Mark revealed at this random time isassumed to satisfied generalised Jacod’s condition.Classical Jacod’s condition concerns initial enlarge-ments and says that the conditional law of a ran-dom variable w.r.t. elements of a reference filtra-tion is absolutely continuous w.r.t. its unconditionallaw. Our relaxation of Jacod’s condition accounts forthe dynamic structure of the problem. In this set-upwe study classical filtration enlargements questionssuch as semimartingale decomposition. This frame-work allows up to recover initial enlargement underJacod’s condition as well as progressive enlargementwith a thin random time.

8.2. Convex duality in robust hedging and optimalstopping problemsIvan Guo (Monash University)

13:55 Wed 4 December 2019 – 182

Dr Ivan Guo

We introduce a generalisation of the classical mar-tingale optimal transport problem that relaxes theusual marginal distribution constraints to arbitrarypath-dependent constraints on the space of proba-bility measures. Strong convex duality is established,which directly leads to a path-dependent Hamilton-Jacobi-Bellman equation in which the solution lo-calises to the state variables of the constraints, whilebypassing the usual dynamic programming princi-ple.

We then show how various pricing-hedging dualityresults in robust hedging and optimal stopping canbe inferred from our convex duality result. More-over, by combining it with extremal point argumentson the space of measures on stopped paths, we dis-cuss how this technique can be applied to the prob-lem of robust hedging American options in continu-ous time.

8.3. Vulnerable American Contracts withExtraneous Risks and Market FrictionsEdward Kim (The University of Sydney)

17:15 Wed 4 December 2019 – 182

Mr Edward Kim

We formulate the problem of valuing American-typecontracts under two non-standard features: (1)

There is an extraneous non-hedgeable event. Whenthe event occurs, the contract is terminated and arecovery payoff is paid instead of the contractedpayoff profile. (2) There are trading frictions (e.g.diverging borrowing and lending rates, collateralobligations under the contract financed by theportfolio) so that the dynamics of self-financingportfolios are no longer linear. As we use an arbi-trage approach to valuation, we propose definitionsof "arbitrage" and "superhedging the claim". Undercertain market conditions, the problem can be char-acterised as a nonlinear optimal stopping problem,or the solution of a reflected backward stochasticdifferential equation.

8.4. Mean-field stable CIR processLibo Li (University of New South Wales)

13:30 Thu 5 December 2019 – 182

Libo Li

We study the strong well-posedness as well as thenumerical approximation of a one-dimensionalstable driven stochastic differential equation withmean field interaction in the drift. The work ismotivated by the study of contagion behaviors indefault and interest rates modelling.

8.5. Non-Markovian Multidimensional QuadraticBSDEKihun Nam (Monash University)

14:20 Wed 4 December 2019 – 182

Dr Kihun Nam

Xing and Zitkovic (2018) recently proved the exis-tence and uniqueness of solution for a system ofquadratic backward stochastic differential equa-tions (BSDE) under Markovian set-up using PDE.The driver of the system is assumed to satisfy theBensoussan–Frehse (BF) condition. The solutionof such a system corresponds to the Nash equilib-rium in stochastic differential game or price impactmodel. In this talk, based on probabilistic argument,we will present the existence and uniqueness resultunder the non-Markovian setting with BF condition.

8.6. Portfolio optimization with a prescribedterminal wealth density by deep optimal transportWEI Ning (Monash University)

13:30 Wed 4 December 2019 – 182

Miss WEI Ning

This paper aims at steering the portfolio wealth froman initial distribution to a prescribed distribution atthe terminal time, via controlling the portfolio al-location process. We study this problem under theframework of Optimal Mass Transport, and we pro-vide a duality result for it. Numerically, we solve the

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dual problem by seeking for the optimal potentialfunction with a finite difference method, and we di-rectly solve for the allocation process in the primalproblem with a deep learning method. Then nu-merical examples for various target terminal distri-butions are given, showing that we can successfullyreach the attainable targets.

8.7. Robust finance: data-driven approach topricing, hedging and risk managementJan Obloj (University of Oxford)

15:35 Wed 4 December 2019 – 182

Prof Jan Obloj

How do we quantify the impact of making assump-tions? How do we value information (data)? Howdo we capture the interplay between risk (describedby a familiar model) and uncertainty (about themodel itself)? In this talk I introduce the robustparadigm which strives to answer such questions.The framework is designed to interpolate betweenmodel-independent and model-specific settingsand to allow to address and quantify the model risk.I explain briefly how classical fundamental notionsand theorems in quantitative finance extend to therobust setting. I then focus on simple concreteexamples. I use vanilla option prices, together withagent-prescribed bounds on key market character-istics, to drive the interval of no-arbitrage prices andthe associated hedging strategies. The setting can beseen as a constrained variant of the classical optimaltransportation problem and comes with a naturalpricing-hedging duality. I discuss numerical meth-ods based on discretisation and LP implementationbut subsequently focus on a deep NN optimisation.Finally, I look at ways to coherently combine optionprices data with past time series data, leading toa dynamic robust risk estimation. I explain howsuch non-parametric statistical estimators of keyquantities (e.g., superhedging prices, 10-days V@R)superimposed with option prices can be treated asinformation signals.

8.8. Path Independence of Exotic Options andConvergence of Binomial ApproximationsKenneth James Palmer (National Taiwan University)

14:45 Wed 4 December 2019 – 182

Prof Kenneth James Palmer

This is joint work with Guillaume Leduc. We presentways in which barrier and lookback options can beregarded, in some sense, as path-independent op-tions. For both kinds of options, the usual binomialapproach yields convergence of order n−1/2, where nis the number of periods, but our path-independentpricing yields convergence of order 1/n.

8.9. Calibration of Local-Stochastic Volatilitymodels by Optimal TransportShiyi Wang (Monash University)

16:25 Wed 4 December 2019 – 182

Ivan Guo, Gregoire Loeper, Shiyi Wang

In this paper, we study a semi-martingale optimaltransport problem and its application to the cali-bration of Local-Stochastic Volatility (LSV) models.Rather than considering the classical constraints onmarginal distributions at initial and final time, weoptimise our cost function given the prices of a fi-nite number of European options. We formulatethe problem as a convex optimisation problem, forwhich we provide a dual formulation. Then we solvenumerically the dual problem, which involves a fullynon-linear Hamilton-Jacobi-Bellman equation. Themethod is tested by calibrating a Heston-like LSVmodel with simulated data and foreign exchangemarket data.

8.10. Multiscale Linear-Quadratic StochasticOptimal ControlJames Yang (The University of Sydney)

16:50 Wed 4 December 2019 – 182

Mr James Yang

In this talk, we consider a quadratic optimisationproblem driven by a multiscale linear stochastic dif-ferential equation with multiplicative noise. Suchproblems are motivated by models with slow-fastdynamics and reducing the dimensional complex-ity. In particular, interesting observations can bemade by considering the convergence problem asthe speed of the slow and fast dynamics diverge.This can be done by applying singular perturba-tion theory to the differential Riccati equation. Asa result, we are able to construct approximating op-timal controls and value function, which are of alower dimensional complexity. Finally, we discussthe optimal control problem when the noise is addi-tive. In this case, we can show that the approximatevalue function is composed of value functions fromtwo subproblems; another linear-quadratic optimi-sation problem and an ergodic control problem.This is a joint work with Ben Goldys (USyd), Gian-mario Tessitore (Uni of Milano-Bicocca) and ZhouZhou (USyd).

8.11. On the Notions of Equilibria forTime-inconsistent Stopping Problems inContinuous TimeZhou Zhou (The University of Sydney)

14:20 Thu 5 December 2019 – 182

Erhan Bayraktar, Jingjie Zhang, Zhou Zhou

A new notion of equilibrium, which we call strongequilibrium, is introduced for time-inconsistentstopping problems in continuous time. Comparedto the existing notions introduced in [Huang &

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Nguyen-Hu, 2018] and [Christensen & Lindensjo,2018], which in this paper are called mild equilib-rium and weak equilibrium respectively, a strongequilibrium captures the idea of subgame perfectNash equilibrium more accurately. When the stateprocess is a continuous-time Markov chain andthe discount function is log sub-additive, we showthat an optimal mild equilibrium is always a strongequilibrium. Moreover, we provide a new iterationmethod that can directly construct an optimal mildequilibrium and thus also prove its existence.

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9. Functional Analysis, Operator Algebra, Non-commutative Geometry

9.1. Isomorphisms of AC (σ) spaces.Shaymaa Shawkat Kadhim Al-shakarchi (University

of New South Wales)

16:00 Tue 3 December 2019 – 134

Mrs Shaymaa Shawkat Kadhim Al-shakarchi

A theorem of Gelfand and Kolmogoroff in 1939 as-serts that, the compact spaces X and Y are home-omorphic if and only if the algebras of continuousfunctions C (X ) and C (Y ) are isomorphic as algebras.In 2005, the algebras of absolutely continuous func-tions AC (σ) was defined by Doust and Ashton on acompact subset σ of the complex plane, and theystudied whether there was a similar link for these al-gebras between the properties of the domain σ andthe Banach algebra properties of the function space.In one direction Doust and Leinert (2015) showedthat if AC (σ1) is algebra isomorphic to AC (σ2) thenσ1 and σ2 must be homeomorphic, so the interestnow is in examining the converse implication.

In general the answer is no. We have examplesof infinite families of homeomorphic spaces σn forwhich the corresponding AC (σn) spaces are mutu-ally nonisomorphic. On the other hand, if one onlyconsiders sets σ lying in restricted families, thenone can obtain positive results. Doust and Leinertshowed that if the setsσ1 andσ2 are polygonal com-pact subsets of the plane then AC (σ1) is algebra iso-morphic to AC (σ2). Then in our research we havecontinued addressing the Gelfand-Kolmogorff theo-rem in a class of functions spaces AC (σ) by inves-tigating the algebraic structure of functions on a dif-ferent types of compact setsσwhereσ is finite unionof line segments and finite union of convex edges.

9.2. Higher twisted K-theoryDavid Leonard Brook (The University of Adelaide)

15:35 Tue 3 December 2019 – 134

Mr David Leonard Brook

Higher twisted K-theory is a recent generalisation oftopological K-theory stimulated by results of UlrichPennig and Marius Dadarlat, who use an operatoralgebraic approach to provide geometric represen-tatives for all abstract twists of K-theory. It involvesa larger class of twists than Rosenberg’s twisted K-theory - which has ties to string theory - and as suchit is expected to be of physical interest in the realmof M-theory. In this talk, I will present an intro-duction to higher twisted K-theory and explain whythis new construction is expected to yield meaning-ful results. In particular, I will outline computationaltechniques including the Mayer-Vietoris sequenceand a twisted Atiyah-Hirzebruch spectral sequence,and present constructions of explicit geometric rep-resentatives for twists in special cases.

9.3. Some geometric constants for Morrey spacesHendra Gunawan (Bandung Institute of Technology)

13:30 Fri 6 December 2019 – 134

Prof Hendra Gunawan

In this talk we shall discuss three geometric con-stants, namely the von Neumann-Jordan constant,the James constant, and the Dunkl-Williams con-stant, for Morrey spaces. These constants measureuniformly non-squareness of the spaces. We shallsee that the three constants are the same as those forL1 and L∞ spaces, which show that Morrey spacesare not uniformly non-square. The work is joint withE. Kikianty, Y. Sawano, and C. Schwanke.

9.4. The talented monoid of a directed graphRoozbeh Hazrat (Western Sydney University)

13:55 Fri 6 December 2019 – 134

Prof Roozbeh Hazrat

We associate an abelian monoid to a direct graph.We show how this monoid beautifully captures thegeometry of the graph! The hope is that this monoidwould be a complete invariant for a class of algebracalled Leavitt path algebras.

9.5. Fredholm Property of Operators from 2DString Field TheoryHai-Long Her (The Australian National University)

15:10 Tue 3 December 2019 – 134

Prof Hai-Long Her

In a recent study of Landau-Ginzburg model ofstring field theory, there appears a type of perturbedCauchy-Riemann equation, i.e. the zeta-instantonequation. Solutions of zeta-instanton equation havedegenerate asymptotics. This degeneracy is a severerestriction for obtaining the Fredholm propertyand constructing relevant homology theory. In thisarticle, we study the Fredholm property of a sort ofdifferential operators with degenerate asymptotics.As an application, we verify certain Fredholm prop-erty of the linearized operator of zeta-instantonequation.

9.6. Inversion of operator pencils on Banach spaceusing Jordan chainsGeetika Verma (University of South Australia)

14:20 Fri 6 December 2019 – 134

Dr Geetika Verma

In this talk, I will discuss the inversion of operatorpencils on Banach spaces. The main aim is to finda basic solution to the fundamental equations andhence construct a Laurent series representation forthe resolvent operator on the given annulus. As-suming that the generalized resolvent operator has

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9. Functional Analysis, Operator Algebra, Non-commutative Geometry

an isolated essential singularity and that it is an-alytic on some annular region centred at the sin-gularity and further assume—without loss of gen-erality—that the singularity is located at the origin.On each such annular region, I will show that thecomplementary projections which separate the twocomponents of the spectral sets are uniquely deter-mined by the generating subspaces for the associ-ated infinite-length Jordan chains. I will use theseJordan chains to find the key projection operatorsand thereby obtain the desired direct sum decom-positions for the domain and range spaces.

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10.1. The prescribed Ricci curvature problem fornaturally reductive metrics on compact Lie groups:general theoryRomina Melisa Arroyo (University of Queensland)

16:00 Wed 4 December 2019 – 136

Dr Romina Melisa Arroyo, Dr Artem Pulemotov

An interesting open problem is to find a Riemann-ian metric whose Ricci curvature is prescribed, thatis, a Riemannian metric g and a real number c > 0satisfying

Ric(g ) = cT,

for some fixed symmetric (0,2)-tensor field T on amanifold M , where Ric(g ) denotes the Ricci curva-ture of g .

The aim of this talk is to discuss this problem withinthe class of naturally reductive metrics when M is acompact simple Lie group, and present recently ob-tained results in this setting.

This talk is based on work in progress with ArtemPulemotov (The University of Queensland).

10.2. Hyperbolic 3-manifolds, embeddings and aninvitation to the Cross Curvature FlowPaul Bryan (Macquarie University)

13:55 Wed 4 December 2019 – 136

Mr Paul Bryan

Hyperbolic three manifolds, particularly those of fi-nite volume, are important in the study of three-manifold topology. Out of the eight geometries aris-ing in Thurston’s geometrisation program, only thehyperbolic ones are not explicitly. The cross cur-vature flow was introduced by Hamilton and Chowas a promising tool for negatively curved metrics tohyperbolic metrics. There is a natural integrabil-ity condition ensuring isometric embeddability inMinkowksi space as a spacelike co-compact hyper-surface in which case the cross curvature flow isequivalent to the Gauss curvature flow. By Andrewset. al. the situation is completely understood withsmooth convergence to a hyperbolic metric. Thegeneral case remains an open problem, yet some re-sults are known in favour of the general case such asstability of the hyperbolic metric due to Knopf andYoung as well as monotone quantities.

10.3. Existence of sharp asymptotic profiles ofsingular solutions to an elliptic equation with asign-changing nonlinearityFlorica Corina Cirstea (The University of Sydney)

16:25 Tue 3 December 2019 – 136

Florica C. Cîrstea, Frédéric Robert and Jérôme Vétois

In this talk, I will discuss recent joint work withFrédéric Robert (University of Lorraine) and JérômeVétois (McGill University) in which we settle the

open question of the actual existence of all the sin-gular profiles ascertained earlier by the speaker withF. Robert [Proc London Math Soc, 114 (2017)] for thepositive smooth solutions to the nonlinear ellipticequation

−∆u = u2∗(s)−1

|x|s −µuq in BR (0) \ 0.

Here, BR (0) denotes the open ball of radius R cen-tred at 0 in Rn for n ≥ 3, µ > 0, q > 1, s ∈ (0,2) and2∗(s) := 2(n − s)/(n −2).

10.4. The fundamental gap in a negatively curveddomainJulie Clutterbuck (Monash University)

14:20 Wed 4 December 2019 – 136

T Bourni, J Clutterbuck, XH Nguyen, A Stancu, G Wei, V

Wheeler

I will give an example of a negatively curved domainin which the fundamental gap— the difference be-tween the first two eigenvalues– behaves quite dif-ferently to the flat or positively curved cases. Fur-thermore, the first eigenfunction fails to possess theproperty of quasi-convexity.

10.5. Symmetric biharmonic mapsMatthew Kevin Cooper (University of New England)

14:20 Fri 6 December 2019 – 136

Matthew Cooper, Andreas Gastel

Biharmonic maps are higher-order analogues toharmonic maps. They are solutions to a fourth-order elliptic PDE, as opposed to a second-orderequation in the harmonic map case. Similarly toharmonic maps, biharmonic maps relate to ap-plications in continuum mechanics and materialsscience, and geometry, to name just two. Theapproach we take to building an understandingof biharmonic maps is to study them in highly-symmetric situations. This reduces the fourth-orderelliptic PDE to a fourth-order ODE. Through this wefind interesting connections to higher-order Hamil-tonian dynamics. In this talk, I will give a motivatingintroduction to biharmonic maps, and then talkabout the techniques I and co-authors have devel-oped in order to study the resulting fourth-orderODE, and how this relates to interesting biharmonicmaps.

10.6. A free boundary problem driven by thebiharmonic operatorSerena Dipierro (The University of Western Australia)

13:30 Wed 4 December 2019 – 136

Assoc Prof Serena Dipierro

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In this talk we review some recent results obtained incollaboration with A. Karakhanyan and E. Valdinociconcerning a new type of free boundary problem in-volving the biLaplacian. In particular, we discuss theanalytic and geometric properties of the minimisers.

10.7. Singular quasilinear elliptic equations withgradient dependent nonlinearitiesMaria Farcaseanu (The University of Sydney)

17:40 Tue 3 December 2019 – 136

Dr Maria Farcaseanu

We obtain Liouville type results for quasilinear el-liptic equations with singular potentials and gra-dient dependent nonlinearities. Furthermore, wealso analyse the behaviour near zero for the pos-itive solutions of such equations. This is a jointwork with Florica Cîrstea and supported by the ARCDP190102948.

10.8. Existence Results for Nonlinear FractionalDifferential EquationsNicholas Fewster-Young (University of South Australia)

17:15 Tue 3 December 2019 – 136

Mr Nicholas Fewster-Young

The study of fractional differential equations hasbeen a field of research which has sparked huge in-terest over at least the last 20 years due its applica-tions in modelling real world phenomena, in suchareas of Cancer research, Biology, Physics and En-gineering. Fractional Calculus was first introducedby Leibniz in 1695 to generalised integer derivativesto non-integer derivatives. This lead to differentialequations and the research of understanding qual-itative and quantitative behaviour of these dynam-ical systems. The theory is dense and well coveredin the case of linear fractional differential equations,however, the nonlinear scenarios which are morecomplex, face challenges and in particular the com-mutative nature of the derivatives. One of the firststeps and a main goal is to understand the qualita-tive nature of nonlinear fractional differential equa-tions such that they are useful for modelling. Themain aim of this talk is to present novel existence re-sults and a priori bounds on solutions to nonlinearcase where the order is between 1 and 2 by the use oftopological methods.

10.9. Global methods for semi-linear hyperbolicequationsJesse Gell-Redman (AMSI/University of Melbourne)

14:20 Tue 3 December 2019 – 136

Dr Jesse Gell-Redman

I will describe several results related to small dataexistence for inhomogeneous semi-linear hyper-bolic equations which utilise the groundbreakingmethod, pioneered by Andras Vasy, in which one

constructs propagators for linear hyperbolic op-erators using global propagation of singularitiesestimates.

10.10. Ill-posedness of the Camassa-Holm andrelated equations in the critical spaceZihua Guo (Monash University)

13:55 Fri 6 December 2019 – 136

Zihua Guo, Xingxing Liu, Luc Molinet, Zhaoyang Yin

We prove norm inflation and hence ill-posednessfor a class of shallow water wave equations, suchas the Camassa-Holm equation, Degasperis-Procesiequation and Novikov equation etc., in the criticalSobolev space H 3/2 and even in the Besov space

B 1+1/pp,r for p ∈ [1,∞],r ∈ (1,∞]. Our results cover

both real-line and torus cases (only real-line case forNovikov).

10.11. Singularities of Axially Symmetric VolumePreserving Mean Curvature FlowSevvandi Priyanvada Kandanaarachchi (Monash

University)

15:35 Fri 6 December 2019 – 136

Dr Sevvandi Priyanvada Kandanaarachchi

We investigate the formation of singularities for sur-faces evolving by volume preserving mean curvatureflow. For axially symmetric flows - surfaces of revo-lution - in R3 with Neumann boundary conditions,we prove that the first developing singularity is ofType I. The result is obtained without any additionalcurvature assumptions being imposed, while axialsymmetry and boundary conditions are justifiablegiven the volume constraint. Additional results andingredients towards the main proof include a non-cylindrical parabolic maximum principle, and a se-ries of estimates on geometric quantities involvinggradient, curvature terms and derivatives thereof.These hold in arbitrary dimensions.

10.12. Quantitative comparison theorems ingeometryKwok-Kun Kwong (University of Wollongong)

15:10 Fri 6 December 2019 – 136

Dr Kwok-Kun Kwong

The classical volume comparison states that undera lower bound on the Ricci curvature, the volumeof the geodesic ball is bounded from above by thatof the ball with the same radius in the model space.On the other hand, counterexamples show that theassumption on the Ricci curvature cannot be weak-ened to a lower bound on the scalar curvature, whichis the average of the Ricci curvature. In this talk, Iwill show that a lower bound on a weighted averageof the Ricci curvature is sufficient to ensure volumecomparison. In the course I will also show a sharpquantitative volume estimate, an integral version of

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the Laplacian comparison theorem, and some appli-cations. If time allows, I will also present some ex-tensions of the theorem.

10.13. A fully nonlinear flow of three-convexhypersurfacesStephen Lynch (University of Tubingen)

15:35 Wed 4 December 2019 – 136

Stephen Lynch

We will discuss a fully nonlinear geometric flowof three-convex hypersurfaces, where the normalspeed at each point of the solution is given by aconcave function of the second fundamental form.Three-convexity means that at each point, thesum of the smallest three principal curvatures ispositive. This flow smoothly deforms any com-pact three-convex initial hypersurface, preservingthree-convexity, until its curvature becomes un-bounded. Our main result is a convexity estimate,which says that high-curvature regions are approx-imately convex. Such an estimate is known to holdfor mean-convex mean curvature flow, and for alarge class of fully nonlinear flows where the speedfunction is convex. For concave speeds, previousresults of this kind assume two-convexity, and makeessential use of this property.

10.14. The Semilinear Calderon Problem onComplex ManifoldsYilin Ma (The University of Sydney)

16:00 Tue 3 December 2019 – 136

Mr Yilin Ma

The study of the Calderon inverse problems havebeen extended to the semilinear case on openbounded domains of real spaces. However, resultstowards the direction of manifolds have been ratherlimited.

We begin by formulating the classical Calderonproblem. Roughly speaking, the Calderon prob-lem is the determination of coefficients in theSchrodinger operator from boundary measure-ments.

We will show that, solving the semilinear Calderonproblem under analytic conditions prescribed onthe coefficients of the associated Schrodinger oper-ator reduces the problem to solving the linearizedCalderon problem. This is equivalent to findingsufficiently many harmonic functions. In the casewhere only partial measurements on the boundaryare available, these harmonic functions would be re-quired to vanish everywhere on the boundary expecton a small open set. This constitutes the main diffi-culty of the problem.

10.15. The prescribed Ricci curvature problem fornaturally reductive metrics on compact Lie groups:examplesArtem Pulemotov (The University of Queensland)

16:25 Wed 4 December 2019 – 136

Dr Artem Pulemotov

Let G be a compact Lie group. Naturally reduc-tive left-invariant metrics form an important class ofRiemannian metrics on G (we denote it Mnat) nestedbetween the class of all left-invariant metrics and theclass of bi-invariant ones. In the talk, we discuss theprescribed Ricci curvature equation Ric g = cT as-suming T ∈Mnat. The unknowns here are the metricg and the scaling factor c. After a quick review of thegeneral theory, we will focus on examples that ex-plain the nature of solutions and reveal several sur-prising phenomena. Joint work with Romina Arroyo(The University of Queensland).

10.16. Higher-order Cheeger and Buserinequalities, and a dynamics applicationChristopher P Rock (UNSW Sydney)

15:35 Tue 3 December 2019 – 136

Mr Christopher P Rock

Higher-order Cheeger constants describe how effi-ciently a manifold can be separated into k largepieces using small cuts. These have been provento be equivalent to the kth eigenfunction of the(optionally weighted) Laplacian up to polynomi-als in k, on geodesically convex manifolds withnon-negative Bakry-Emery Ricci curvature. Wewill present new bounds which apply to manifoldswith negative Ricci curvature bounds and whichdo not depend on k, but will instead depend onthe dimension of the manifold and the Lipschitzconstant of the weight, or on the number of nodaldomains in an eigenfunction. We apply these resultsto justify an algorithm for finding coherent sets intime-varying dynamical systems, i.e. dynamicallyseparated subsets of the phase space. Coherentsets are identified using a dynamic version of thehigher-order Cheeger constants. They are detectedusing eigenfunctions of the weighted Laplacian fora modified metric, called the dynamic Laplacian.

10.17. On the stability of expanding black holespacetimesVolker Schlue (The University of Melbourne)

15:10 Tue 3 December 2019 – 136

Dr Volker Schlue

In the context of Einstein’s equations with positivecosmological constant, the Kerr de Sitter family ofsolutions are a model of a black hole in the expand-ing universe. In this talk, I will focus on a stabilityproblem for the expanding region, which can be for-mulated as a characteristic initial value problem tothe future of the cosmological horizons. I will briefly

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summarise my work on the decay of the conformalWeyl curvature in this setting, and present recentprogress on the global construction of optical func-tions in de Sitter, and describe their relevance for myapproach to this problem in double null gauge.

10.18. An epiperimetric inequality approach to theparabolic Signorini problemWenhui Shi (Monash University)

14:45 Wed 4 December 2019 – 136

Ms Wenhui Shi

In this talk I will discuss an epiperimetric inequalityassociated to the parabolic Signornini problem, andshow how it can be used to study the asymptotic be-havior of the solution around certain free boundarypoints, as well as the regularity of the free boundary.

10.19. Nonlocal minimal graphs in the plane aregenerically stickyEnrico Valdinoci (The University of Western Australia)

13:30 Fri 6 December 2019 – 136

Prof Enrico Valdinoci

We prove that nonlocal minimal graphs in the planeexhibit generically stickiness effects and boundarydiscontinuities. More precisely, we show that if anonlocal minimal graph in a slab is continuous upto the boundary, then arbitrarily small perturbationsof the far-away data produce boundary discontinu-ities. Hence, either a nonlocal minimal graph is dis-continuous at the boundary, or a small perturba-tion of the prescribed conditions produces bound-ary discontinuities. The proof relies on a slidingmethod combined with a fine boundary regularityanalysis, based on a discontinuity/smoothness al-ternative. Namely, we establish that nonlocal min-imal graphs are either discontinuous at the bound-ary or their derivative is Hölder continuous up to theboundary. In this spirit, we prove that the boundaryregularity of nonlocal minimal graphs in the plane"jumps" from discontinuous to differentiable, withno intermediate possibilities allowed. In particu-lar, we deduce that the nonlocal curvature equationis always satisfied up to the boundary. These re-sults have been obtained in collaboration with Ser-ena Dipierro and Ovidiu Savin.

10.20. Horospherically convex geometry inhyperbolic space and geometric flowsYong Wei (Australian National University)

17:15 Wed 4 December 2019 – 136

Dr Yong Wei

I will introduce some geometric structures of horo-spherically convex hypersurfaces in hyperbolicspace, including horospherical support function,horospherical Gauss map and hyperbolic principalcurvature radii, which can be viewed as hyperbolicanalogue of the convex geometry in Euclidean

space. Then I will discuss some results on geometricflows driven by smooth functions of hyperbolicprincipal curvature radii.

10.21. Counterexamples to graph preservationunder mean curvature flowValentina-Mira Wheeler (University of Wollongong)

16:50 Wed 4 December 2019 – 136

Dr Valentina-Mira Wheeler

Mean curvature flow is the steepest descent gradientflow for the area functional, making it a difficult flowto obtain a long time existence result for geometricobjects that flow without an additional restriction.One can see this in a “simple” way by using convexobjects as barriers. The celebrated result of Huiskenshowing that convex bodies under mean curvatureflow will shrink out of existence in finite time allowsus to prove the extinction of any other object con-tained inside (in the case they do not become nonsmooth before that). One property of the solutionthat facilitates the long time existence proof is that ofbeing graphical. A mean curvature flow solution thatis graphical is equivalent to a second order quasilin-ear strictly parabolic partial differential equation forwhich one can employ parabolic methods to obtainlong time existence. Under graphicality Ecker andHuisken proved in ’89 that entire solutions of themean curvature flow exist for all times. For bound-ary value problems one has to consider further argu-ments to manage maintaining initial graphicality upto and including the boundary. In this short talk weshow that for hypersurfaces moving by mean curva-ture flow with free boundary, preservation of graphi-cality holds only in very special circumstances. Thatis we prove that for any non-cylindrical smooth sup-port hypersurface there exist smooth mean curva-ture flows with graphical initial data and free bound-ary on this hypersurface that become non-graphicalin finite time. This is joint work with Ben Andrews(ANU).

10.22. Short time existence for higher ordercurvature flows with and without boundaryconditionsYuhan Wu (University of Wollongong)

16:50 Tue 3 December 2019 – 136

Ms Yuhan Wu

We prove short time existence for higher order cur-vature flows of plane curves with and without gener-alised Neumann boundary condition and describehow these results fit into a broader framework foranalysis of the behaviour of these flows.

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11. Geometry including Differential Geometry

11.1. On the signature of the Ricci curvature onnilmanifoldsRomina Melisa Arroyo (University of Queensland)

15:35 Tue 3 December 2019 – 186

Dr Romina Melisa Arroyo, Dr Ramiro Augusto Lafuente

One of the most important challenges of Riemann-ian geometry is to understand the Ricci curvature. Aproblem that is still open is: determine all possiblesignatures of the Ricci curvature of all Riemannianmetrics on a given manifold. The aim of this talk isto present the problem in the setting of nilpotent Liegroups with left-invariant metrics, and give an an-swer in the case that the nilpotent Lie group admitsa nice basis.

This talk is based on work in progress with RamiroLafuente (The University of Queensland).

11.2. Positive curvature in dimension sevenOwen Dearricott (The University of Melbourne)

15:35 Fri 6 December 2019 – 186

Dr Owen Dearricott

I will detail a general construction for putting pos-itive sectional curvature on a series of 7-manifoldsdiscussed as viable candidates to carry positivelycurved metrics with co-dimension one principal or-bits discussed by Grove, Wilking and Ziller in JDG in2008 by appropriately modifying a naturally occur-ring 3-Sasakian metric. This builds on previous workwhere I considered isolated examples of this sortwhere the base Bianchi IX self-dual Einstein orbifoldmetric had an algebraic closed form.

11.3. Distinguished curves and integrability inRiemannian and conformal geometryA. Rod Gover (The University of Auckland)

13:55 Thu 5 December 2019 – 183

Prof A. Rod Gover

A new characterisation is described for the un-parametrised geodesics, or distinguished curvesof pseudo-Riemannian and conformal geometry.The characterisation is a type of moving incidencerelation and most importantly it leads naturally to avery general theory and construction of quantitiesthat are necessarily conserved along the curves. (Asused in geometry and geometric analysis as wayof simplifying the problem of determining suchcurves.) In this the usual role of Killing tensors andconformal Killing tensors is recovered, but the con-struction shows that a vastly larger class of equationsolutions can also yield curve first integrals. Next itturns out that the ideas lead to yet one more way tounderstand pseudo-Riemannian geodesics and thishas applications into understanding and treatingthe distinguished curves of structures with singular

metrics such as Poincare-Einstein manifolds andtheir generalisations.

This talk is based on joint work with Daniel Snell andArman Taghavi-Chabert

11.4. Group Extensions and Bundle GerbesParsa Kavkani (The University of Adelaide)

16:00 Tue 3 December 2019 – 186

Mr Parsa Kavkani

Line bundles on a manifold M provide a geometricrealisation of the second integral cohomology of Mvia their chern class. Similarly bundle gerbes pro-vide a geometric realisation of the third integral co-homology of M via their Dixmier-Douady class. Animportant example of bundle gerbes is the liftingbundle gerbe. In this talk I will review some con-structions of groups extensions, introduce the no-tion of bundle gerbe and explain how the lifting bun-dle gerbe is associated to group extensions.

11.5. Rolling Symmetric SpacesKrzysztof Krakowski (Cardinal Stefan Wyszynski

University in Warsaw)

14:20 Fri 6 December 2019 – 186

Dr Krzysztof Krakowski

Mechanical model of a surface rolling upon anotherone, without a slip or twist, both embedded in R3,serves as the most classical non-holonomic differ-ential system with a (2,3,5) distribution D . It iswell known that given a curve on one of these sur-faces, there always exists the unique rolling map,that traces the point of contact along that curve.

I shall discuss the simple case of a symmetric spacerolling upon a hyperplane, both embedded in Eu-clidean or pseudo-Euclidean space. These systemsdraw many similarities with the classical example ofa sphere rolling upon a plane, and may be describedin terms of Lie algebra. However, somewhat surpris-ing is the way these symmetric spaces should be em-bedded. I shall illustrate recent results with somesimple and some, perhaps, not so simple examples.

11.6. Conservation laws and parabolicMonge-Ampere equationsBenjamin Blake McMillan (The University of Adelaide)

13:30 Thu 5 December 2019 – 183

Dr Benjamin Blake McMillan

In this talk, I will describe how the geometry ofan arbitrary parabolic second order equation gov-erns the existence of its conservation laws, and con-versely, how the existence of even a single conser-vation law puts strong geometric restrictions on aparabolic equation. In particular, I will describe the

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strong connection between conservation laws andparabolic Monge-Ampere equations.

11.7. On cylindricity of submanifolds ofnonnegative Ricci curvature in a Minkowski spaceYuri Nikolayevsky (La Trobe University)

13:30 Fri 6 December 2019 – 186

Dr Yuri Nikolayevsky

By the Splitting Theorem of Cheeger-Gromoll,a complete Riemannian manifold M n of non-negative Ricci curvature which contains a line (acomplete geodesic every arc of which minimises thedistance between its endpoints) is the Riemannianproduct N n−1 ×R. The counterpart of this result insubmanifold geometry is as follows: a complete Rie-mannian submanifold M n ⊂ Rn+p of non-negativeRicci curvature which contains a line (of Rn+p ) is thecylinder N n−1 ×R⊂Rn+p−1 ×R.

A direct translation of these results to the Finsler set-tings by replacing the Euclidean ambient space bya Minkowski space and the Ricci curvature, by theRicci curvature of the induced Finsler metric on thesubmanifold, most likely, does not work. The rea-son for that is the fact that in Finsler geometry, theconnection between the Ricci (or the flag) curvatureof a submanifold and its shape is much weaker thanthat in Riemannian geometry. For example, we con-structed an example of a (locally) strictly saddle sur-face of positive flag curvature in a three-dimensionalMinkowski space.

We consider submanifolds of non-negative Riccicurvature in a Minkowski space which contain aline or whose relative nullity index is positive. Forhypersurfaces, submanifolds of codimension two orof dimension two, we prove that such a submanifoldis a cylinder, under certain conditions on the inertiaof the pencil of the second fundamental forms.

This is a joint work with A.Borisenko.

11.8. Superintegrable systemsJeremy Nugent (University of New South Wales)

17:15 Tue 3 December 2019 – 186

Mr Jeremy Nugent

TBA

11.9. Locally conformal Käler or symplecticstructures on compact solvmanifoldsMarcos Origlia (Monash University)

15:10 Fri 6 December 2019 – 186

Dr Marcos Origlia

We study locally conformal Kähler (LCK) manifolds,that is, a Hermitian manifold (M , J , g ) such that oneach point there exists a neighborhood where themetric is conformal to a Kähler metric. Equivalently,

(M , J , g ) is LCK if and only if there exists a closed 1-form θ such that dω = θ∧ω, where ω is the funda-mental 2-form determined by the Hermitian struc-ture. The 1-form θ is called the Lee form. On theother hand, the concept of LCK structure can begeneralized to the notion of locally conformal sym-plectic (LCS) structure, that is a pair (ω,θ) satisfyingdω= θ∧ω, where ω is a non-degenerate 2-form andθ is a closed 1-form.

In this talk, we discuss left-invariant LCK or LCSstructures on solvable Lie groups and the existenceof lattices (co-compact discrete subgroups) on theseLie groups in order to obtain compact solvmanifoldsequipped with these kinds of locally conformal geo-metric structures.

11.10. The prescribed Ricci curvature equation on(SU (2)×SU (2))/U (1)r

Artem Pulemotov (The University of Queensland)

15:10 Tue 3 December 2019 – 186

Dr Artem Pulemotov

Let T be a positive-definite G-invariant (0,2)-tensorfield on a homogeneous space G/H . We discussthe prescribed Ricci curvature equation Ric g = cT ,where the unknowns are the Riemannian metric gon G/H and the positive number c. Solutions to thisequation are critical points of the scalar curvaturefunctional subject to a trace constraint. We presenttheir complete classification assuming G = SU (2)×SU (2) and H = U (1) with an “asymmetric" embed-ding. Our results provide insights into the behaviourof the scalar curvature functional in the general set-ting. Joint work with Wolfgang Ziller (The Universityof Pennsylvania).

11.11. Kähler manifolds, Sasakian manifolds andgeneralised Taub-NUT solutionsGerd Schmalz (University of New England)

16:50 Tue 3 December 2019 – 186

Gerd Schmalz, Masoud Ganji

The Taub-NUT solution is a Ricci-flat Lorentzianspacetime. It admits a shear free congruence, i.e.a foliation into null-geodesics the flow along whichpreserves the conformal class of the Lorentzian met-rics restricted to perpendicular subspaces. The leafspace of the foliation has a natural CR structure,which in the case of the classical Taub-NUT and Kerrsolutions is Sasakian. Since Sasakian structures areintimately related to Kähler geometry, it is naturalto investigate the relationship between Kähler ge-ometry and Ricci-flat Lorentzian geometry. I willpresent a construction of higher dimensional gener-alisations of the Taub-NUT space related to certainKähler-Einstein manifolds. This is joint work withMasoud Ganji.

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11.12. Second order superintegrable systems inarbitrary dimensionAndreas Vollmer (University of New South Wales)

13:55 Fri 6 December 2019 – 186

Dr Andreas Vollmer

Broadly speaking, second order superintegrablesystems are to date classified for conformally flatgeometries in dimension 2 and 3 only. However, themethods do not carry over to higher dimension, asthe underlying system of partial differential equa-tions quickly grows and becomes tedious to handle.A new, algebraic-geometric approach has recentlybeen suggested by Kress & Schoebel (2019), and wassuccessfully applied to (non-degenerate) secondorder superintegrable systems on 2-dimensionalEuclidean geometry. Extending this approach tosuit any dimension, and non-Euclidean geometries,we can characterize second-order superintegrablesystems (under very mild extra assumptions) bysmooth (0,3)-tensor fields (structure tensors).

These superintegrable structure tensors are gov-erned by a simple set of algebraic equations. Forspaces of constant sectional curvature, the situationsimplifies further, giving rise to two scalar func-tions that characterize the structure tensor. Thisframework lays the groundwork for an algebraic-geometric classification of second-order super-integrable systems in any dimension (joint workwith Jonathan Kress and Konrad Schoebel). Timepermitting, the talk will also address conformallysuperintegrable systems.

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12. Harmonic and Semiclassical Analysis

12.1. Vector-valued time-frequency analysis andthe bilinear Hilbert transformAlex Amenta (University of Bonn)

14:20 Wed 4 December 2019 – 134

Dr Alex Amenta

The bilinear Hilbert transform is a bilinear singularintegral operator which is invariant not only undertranslations and dilations, but also under modula-tions. This additional symmetry turns out to makeproving Lp -bounds especially difficult. I will give anoverview of how time-frequency analysis is used inproving these Lp -bounds, with focus on the recentlyunderstood setting of functions valued in UMD Ba-nach spaces.

12.2. Construction of Multidimensional ProlateSpheroidal Wave FunctionsHamed Baghal Ghaffari (The University of Newcastle)

15:35 Wed 4 December 2019 – 134

Mr Hamed Baghal Ghaffari

We investigate the construction of multidimensionalprolate spheroidal wave functions using techniquesfrom Clifford analysis. The prolates are eigenfunc-tions of a time-frequency limiting operator, but weshow that they are also eigenfunctions of a differen-tial operator. In an effort to compute solutions ofthis operator, we prove a Bonnet formula for a classof Clifford- Gegenbauer polynomials.

12.3. Sharp endpoint estimates for SchrödingergroupsXuan Duong (Macquarie University)

13:30 Wed 4 December 2019 – 134

Prof Xuan Duong

Let L be a non-negative self-adjoint operator satis-fying the generalized Gaussian (p0, p ′

0) estimates oforder m for some 1 ≤ p0 < 2. We proved sharp end-point Lp -Sobolev bound for the Schrödinger groupe i tL that for every p ∈ (p0, p ′

0),∥∥∥(I +L)−s e i tL f∥∥∥

p≤C (1+|t |)s‖ f ‖p , s ≥ n

∣∣1

2− 1

p

∣∣.As a consequence, the above estimate holds for all1 < p <∞ when L satisfies a Gaussian upper bound.This extends classical results due to Feffermann-Stein and Miyachi for the Laplacian on the Euclideanspaces Rn . This is joint work with Peng Chen, Ji Li,Liang Song and Lixin Yan (2018, 2019).

12.4. Weighted Lebesgue and BMO norminequalities for the Calderon and Hilbert operatorsGuillermo Javier Flores (Universidad Nacional de

Cordoba)

16:25 Wed 4 December 2019 – 134

Dr Guillermo Javier Flores

Necessary and sufficient conditions are given forgeneralized Calderon and Hilbert operators to bebounded from weighted Lebesgue spaces into suit-able weighted BMO and Lipschitz spaces. More-over, we have obtained new results on the bounded-ness of these operators from the space of essentiallybounded measurable functions into BMO, even inthe unweighted case for the Hilbert operator. Theclass of weights involved are close to the doublingand reverse Holder conditions related to the Muck-enhoupt classes.

12.5. A Fredholm approach to solving semilinearevolution equationsAndrew Hassell (Australian National University)

13:55 Wed 4 December 2019 – 134

Prof Andrew Hassell

I will talk about a new approach to solving semilin-ear elliptic, and evolution equations of Schrodingerand wave type, using a global Fredholm approachdeveloped recently by Vasy. This is joint work withJesse Gell-Redman, Jacob Shapiro and JunyongZhang.

12.6. Commutators of Cauchy-Szego type integralsfor domains in C n with minimal smoothnessJi Li (Macquarie University)

14:20 Thu 5 December 2019 – 134

Dr Ji Li

We established the characterisations of bounded-ness and compactness for commutators of Cauchy-Szego type integrals for domains in C n with mini-mal smoothness with respect to the BMO and VMOspaces, respectively.

We note that

(1) such Cauchy-Szego type integral is not a standardCalderon–Zygmund operator. Our result is the firstone to provide full characterisations of commutatorsfor singular integrals with non-smooth kernels.

(2) the approach for compactness is new, and it re-covers all previously known results obtained fromthe method of Uchiyama.

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12. Harmonic and Semiclassical Analysis

12.7. An improved heat kernel bound for certainmagnetic Schrodinger operators.Fu Ken Ly (The University of Sydney)

16:50 Wed 4 December 2019 – 134

Dr Fu Ken Ly

We derive an improved heat kernel bound for certainmagnetic Schrodinger operators. The proof utilisesan improved Fefferman-Phong inequality due to B.Ben Ali.

This is joint work with The Anh Bui.

12.8. Non-homogeneous T (1) theorem for singularintegrals on product quasimetric spacesTrang Thi Thien Nguyen (University of South Australia)

16:00 Wed 4 December 2019 – 134

Ms Trang Thi Thien Nguyen

In the Calderón–Zygmund theory of singular inte-grals, the T (1) theorem of David and Journé is oneof the most celebrated theorems. It gives an easily-checked criterion for a singular integral operator Tto be bounded from L2(Rn) to L2(Rn). The setting ofthis classical result is Euclidean space Rn , equippedwith the usual Euclidean metric and Lebesgue mea-sure. In particular, the functions f that the opera-tor T acts on are defined on Rn . Since then, the T (1)theorem has been generalised to various settings.

In this talk, I will discuss our work in progresson generalising the T (1) theorem, that bringstogether three attributes: ‘product space’, ‘quasi-metric’ and ‘non-doubling measure’. Specifically,we prove a T (1) theorem that can be applied tooperators acting on functions defined on productspaces (X1 × X2,ρ1 × ρ2,µ1 × µ2) equipped with aquasimetric ρ1 × ρ2 and an upper doubling mea-sure µ1 ×µ2, which only satisfies an upper controlon the size of balls, but need not be doubling.

12.9. Scattering from infinity for semi-linear waveequations with weak null conditionVolker Schlue (The University of Melbourne)

14:45 Wed 4 December 2019 – 134

Dr Volker Schlue

In this talk I present global existence results back-wards from scattering data for various semilinearwave equations on Minkowski space satisfying the(weak) null condition. These models are motivatedby the Einstein equations in harmonic gauge, andthe data is given in the form of the radiation field.It is shown in particular that the solution has thesame spatial decay as the radiation field along nullinfinity. I will discuss the proof which relies, on onehand on a fractional Morawetz estimate, and on theother hand on the construction of suitable approxi-mate solutions from the scattering data.

12.10. Spectral multipliers without semigroupframework and application to random walksAdam Sikora (Macquarie University)

13:55 Thu 5 December 2019 – 134

Dr Adam Sikora

We discuss spectral multiplier theorems for abstractself-adjoint operators on spaces of homogeneoustype. We work outside the semigroup context.We introduce a restriction type estimates à laStein-Tomas. This allows us to obtain sharp spectralmultiplier theorems and hence sharp Bochner-Rieszsummability results in some situation. As an appli-cation we prove sharp Bochner-Riesz summabilityresults for the random walk on the integer latticeZn .

The talk is based on joint work with Peng Chen, ElMaati Ouhabaz and Lixin Yan.

12.11. Product Hardy space theory on spaces ofhomogeneous type via orthonormal wavelet basesLesley Ward (University of South Australia)

13:30 Thu 5 December 2019 – 134

Assoc Prof Lesley Ward

I will discuss recent joint work with Yongsheng Han,Ji Li and Cristina Pereyra. We establish the theoryof product Hardy spaces defined on product spacesof homogeneous type X = X1 × X2. Here each fac-tor (Xi ,di ,µi ), i = 1, 2, is a space of homogeneoustype in the sense of Coifman and Weiss, in otherwords, a set Xi equipped with a quasi-metric di anda Borel-regular doubling measure µi . We make ex-tensive use of the orthonormal wavelet expansion ofAuscher and Hytönen. No additional assumptionsare made on the quasi-metrics di , nor on the mea-sures µi .

We show that the wavelet expansion convergesfor suitable test functions and distributions. Wedevelop the product Littlewood–Paley theory forappropriate discrete and continuous square func-tions defined in terms of the wavelets. We definethe Hardy spaces H p (X ) and the Carleson mea-sure spaces CMOp (X ), including the special caseBMO(X ) = CMO1(X ), as well as VMO(X ). Weprove the duality relations H 1(X )∗ = BMO(X ) andVMO(X )∗ = H 1(X ). We establish the Calderón–Zygmund decomposition for H p (X ), deduceinterpolation theorems, and develop an atomicdecomposition for H p (X ). I will mention someapplications of our results.

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13. Inclusivity, diversity, and equity in mathematics

13.1. Maths on countryRowena Ball (The Australian National University)

16:00 Tue 3 December 2019 – G61

Assoc Prof Rowena Ball

Deep in the heart of the NW Qld Gulf savannahcountry, in a shed by a water tank at the back of therailway yard, there was a school. During the lateryears of government-enforced racial segregation,from around the 1930s to the 1960s, the schooleducated Aboriginal children. Despite officialindifference, habitually drunken white teachers,and the mile-and-a-half distance from the reserve,the school persisted because Aboriginal parentsand community valued – and have always valued– formal education for their children. That this isespecially the case with maths and science has inrecent years been recognised, with establishmentof the hugely popular regional STEM camps forIndigenous middle-school students, and STEMsummer schools for Year 11 run by universities.In this talk I shall describe some of the associatedmaths outreach and enrichment activities I aminvolved in. I shall also touch on some new researchto elucidate a mathematical transform practised bythe Euahlayi people, and probably other groups.

13.2. Equity considerations and design ofmathematics outreach to schoolsYudhistira Andersen Bunjamin (UNSW Sydney)

16:25 Tue 3 December 2019 – G61

Yudhistira Andersen Bunjamin, Diana Combe, Michael

Denes, Aditya Ganguly, Manzoor Khan, Aldhytha Karina

Sari and many, many others

Recently, we have been designing mathematicsworkshops for primary and secondary schoolstudents, motivated by promoting mathematicalthinking rather than by introducing an amusingarea or application of mathematics. This projecthas a short but eclectic history - beginning with aregional outreach trip and involving an entire AMSIsummer school, several people from Universities inNew South Wales, Victoria and South Australia, thewilling engagement of some staff and students atUNSW and the helpful interest and advice of manyother experts. Some of our developing workshopshave been presented and well-received on variousoccasions, including this year’s AMSI CHOOSE-MATHS Day at UTS in Sydney and on several UNSWScience Faculty regional outreach trips to the NSWCentral West.

In this talk, we will present some aspects of thisdesign and development process and highlight theconsiderations which were made as a result of theequity motivation, including mathematical level,cultural sensitivity and accessibility. In particular,

we will discuss the interaction between the under-lying mathematics and the operational and equityconsiderations of the workshop.

Joint work with Diana Combe, Michael Denes,Aditya Ganguly, Manzoor Khan, Aldhytha KarinaSari and many, many others.

13.3. Diversity at the Olympiads: Culture changein elite competitionBenjamin Burton (University of Queensland)

15:35 Tue 3 December 2019 – G61

Prof Benjamin Burton

The International Olympiad in Informatics is thepremier international competition for secondarystudents in algorithm design. In many ways it isa model global citizen, governed and developedcollaboratively by an international community ofaround 90 countries. However, it suffers from somewell-known diversity problems. These include analarming gender imbalance, plus the fact that somehost countries cannot welcome all members of thecommunity equally, including LGBTIQ participants,or those with diplomatic conflicts.

This talk will examine the history of some of theseproblems, as well past and present work towards so-lutions. These include both formal and grassrootsinitiatives: some developed by the committees thatoversee the olympiad, and some driven directly bythe member countries. Importantly, we are begin-ning to understand that it is not enough to fix thesymptoms, but in many ways we need to change theculture of the competition and the community ofstudents and trainers who inhabit it. To do this ina way that crosses linguistic, cultural and religiousbarriers is a difficult and ongoing challenge.

The speaker has been a part of the Olympiad forthe last 21 years, including 10 years leading the Aus-tralian delegation, and 10 years serving on the scien-tific and administrative committees that oversee theevent.

13.4. CHOOSEMATHS: approaches to increasingfemale participation in advanced schoolmathematicsJulia Collins (Edith Cowan University)

16:50 Tue 3 December 2019 – G61

Dr Julia Collins

The CHOOSEMATHS project (2015-2019) has beena 5-year partnership between the Australian Math-ematical Sciences Institute (AMSI) and the BHPFoundation. It aimed to turn around communityattitudes to, and participation in, mathematics,especially for girls and young women. In this talk Iwill discuss two aspects of the project that I worked

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on: CHOOSEMATHS Days and CHOOSEMATHSMentoring. Both were targeted at female students inYears 9 and 10, and aimed to increase the numbersof students choosing higher levels of mathematicsin Year 11/12 (i.e. Methods and Specialist mathe-matics). CHOOSEMATHS Days were 1-day eventsheld at schools and universities around Australia,while CHOOSEMATHS Mentoring brought togetherstudents and mathematical mentors in small groupswho communicated regularly online. I will discussthe approaches of both programs and will reporton their effectiveness in changing mathematicalattitudes among the participants.

13.5. A call to actionNalini Joshi (The University of Sydney)

15:10 Tue 3 December 2019 – G61

Prof Nalini Joshi

The Australian Mathematical Society establisheda committee on Equity, Diversity and Inclusion in2018. I am the Chair. In this talk, I will explainwhat we have done so far on this committee andwhat is to come. In particular, we have establisheda new named lectureship for the annual AustMSconferences, a new special session (in which thistalk is being delivered) and a code of conduct. Thesehave procedures attached to them and in this talk Iask you to support our call to action.

13.6. Creating a critical mass of females inengineering mathematics classroomsHeather Lonsdale (Curtin University)

15:35 Wed 4 December 2019 – G61

Dr Heather Lonsdale, Assoc Prof Natalie Lloyd, Ms Jolanta

Szymakowski

The Engineering Foundation Year at Curtin Univer-sity has been organised for many years into small co-horts of about 20 students who are all allocated tothe same tutorials and workshop classes for all unitsin their first year. This was initially organised to givestudents a cohort experience with an emphasis oncreating diverse groups that were broadly represen-tative of the larger student enrolment in the course,which meant that the female students were dividedroughly equally throughout all groups with only asmall number in each group.

In 2016, the group organisation was changed toinstead prioritise grouping females into a criticalmass, aiming to have at least 7 females in a groupof 20, for groups where females are present. Therationale for this change was based on researchindicating that gender stereotyping and discrimina-tion is minimised in organisations that had achieved30-35

In this talk we will discuss these cohort arrange-ments, and some of the research and observations

on these cohorts that have fed into the broader lit-erature on the critical mass of females in the class-room.

13.7. Improving accessibility in mathematicsMatthew Mack (Multiple Universities)

14:20 Wed 4 December 2019 – G61

Matthew Mack

Enabling inclusivity and diversity within any pop-ulation also requires attention be paid to ensuringthat activities and events are accessible. Partici-pants with disabilities and/or certain sensitivitiesand preferences may find it difficult to engage withinthese events due to circumstances beyond their con-trol.

In this talk, I will address strategies for both mathe-matics events and teaching that contribute to a moreaccessible environment, drawing from my own ex-periences of being hard-of-hearing and from ob-serving similar practices. We will also look at thebenefits these strategies bring to other people, aswell as the practicalities of implementing them.

13.8. Childcare at a large mathematical conferenceDaniel Mathews (Monash University)

13:55 Wed 4 December 2019 – G61

Dr Daniel Mathews

I’ll discuss some of the issues around organisingchildcare for a large mathematical conference suchas the AustMS meeting, based on some personal ex-perience.

13.9. Descartes was wrong - The psychology ofsafety and its implications to equality, diversity, andinclusionJohn Ormerod (The University of Sydney)

17:15 Wed 4 December 2019 – G61

Dr John Ormerod

The phrase "Cogito, ergo sum" by Descartes, usuallytranslated to "I think therefore I am", and is one ofthe most famous quotes from Western Philosophy.This contrasts with Ubuntu philosophy which states:"I am because we are, and since we are, thereforeI am." The later statement is more consistent withthe science of interpersonal neurobiology which ar-gues that who we are is a composite of the relation-ships that we have with one another. In implication,each other’s psychological safety is dependent uponone other. In turn has huge implications to belong-ing, creativity, and well being. In addition to thiswe discuss the advantages to having a psychologi-cal safe workplace, and the flow on effects to inno-vation, motivation, engagement, and improving di-versity.

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13.10. Responsive Techniques for TeachingAustralian, Indigenous School Students: What PartDoes Culture Play in Teaching Mathematics?Collin Grant Phillips (The University of Sydney)

16:00 Wed 4 December 2019 – G61

Dr Collin Grant Phillips

The Mathematics Learning Centre (MLC) has taughtthe Mathematics component of the STEM work-shops (or Workshops for short) for Indigenousschool students since 2017. The STEM workshopsare conducted by the Faculty of Engineering andInformation Technologies at the University of Syd-ney. This talk will discuss some of the methodsemployed in developing and teaching the Work-shops. In particular, the methods used to evolve theteaching material, content and learning methods ofthe Workshops from the continual and immediateinput from the students will be discussed. Thiswill be demonstrated by outlining how the Codesand Code Cracking sessions of the Workshops havecontinually evolved to respond to the students’input, interests and enthusiasm.

The effect of key pillar concepts of worldview, per-spective, resilience and cultural competence on theteaching of the Workshops and the MLC will be out-lined. The use of these principles for teaching math-ematics from a cultural perspective will also be dis-cussed.

13.11. WIMSIG resources and initiatives tosupport careersJessica Purcell (Monash University)

13:30 Wed 4 December 2019 – G61

Prof Jessica Purcell

I will discuss upcoming, new, and continuing initia-tives by WIMSIG to support women in their careers.These include WIMSIG travel schemes, women inmaths gatherings, a pilot mentoring program, andthe WIMSIG conference, next scheduled for 1-2 Oc-tober 2020 at Monash University.

13.12. Hiring for diversityJacqui Ramagge (The University of Sydney)

14:45 Wed 4 December 2019 – G61

Prof Jacqui Ramagge

I will look at strategies used to increase diversity. Inshort, we are all part of the solution.

13.13. Nurture, gender differences and spatialabilitiesAsha Rao (Royal Melbourne Institute of Technology)

16:25 Wed 4 December 2019 – G61

Prof Asha Rao

As the number of females doing higher mathemat-ics continues to decrease, it is worth consideringhow much of a role nurture plays. I will detail a

comparison done by researchers from California atSan Diego and University of Chicago, on the rolethat nurture plays in promoting gender differencesin spatial abilities.

13.14. Improving the process of organizingconferences and special semestersMarcy Robertson (The University of Melbourne)

16:50 Wed 4 December 2019 – G61

Dr Marcy Robertson

I will describe in detail a new process in hiring andorganizing a recent special semester at the Math-ematical Sciences Research Institute (MSRI) aimedat increasing diversity of gender, geographic loca-tion and mathematics. I will present the parts thatworked, didn’t work, and the impressions of myselfand other organizers.

13.15. Women in mathematics: one perspectiveon things that work so far and things that could bedone in the futureValentina-Mira Wheeler (University of Wollongong)

17:15 Tue 3 December 2019 – G61

Dr Valentina-Mira Wheeler

Gender imbalance in academia and in science hasbeen in the attention of the larger community for awhile now. Mathematics seems to have been espe-cially impacted by this imbalance in the last century.I will give a short, maybe one sided presentation ofthings that I have seen have a positive impact onmodifying that, based on my perspective as a newwoman in mathematics at UOW and in Australia. Iwill also possibly try to outline some avenues thatcould be developed in the future.

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14. Mathematical Biology

14.1. An Algebraic Inversion-Deletion Model forBacterial Genome RearrangementChad Mathew Clark (Western Sydney University)

16:25 Wed 4 December 2019 – 187

Mr Chad Mathew Clark

Reversals are a major contributor to variationamong bacterial genomes, with studies suggestingthat reversals involving small numbers of regionsare more likely than larger reversals. While re-versals of neighbouring regions, otherwise knownas inversions, have been accounted for in boththe signed and unsigned case there has yet to bea model which also accounts for the process ofdeletion without insertion. In this talk, an algebraicmodel of the inversion-deletion process using thesymmetric inverse monoid will be discussed alongwith exact algorithms for reconstructing the mostrecent common ancestor of two genomes arisingby inversions and deletions. This is joint work withAndrew Francis (Western Sydney University), JamesMitchell (University of Saint Andrews) and JuliusJonušas (TU Wien).

14.2. Study of HIV in-host model throughmulti-pathways infection under different blockers :local and global analysisSukhen Das (Jadavpur University)

13:30 Thu 5 December 2019 – 187

Prof Sukhen Das and Nandadulal Bairagi

CD4+ T cells is an important component of ourimmune system. Human immunodeficiency virus(HIV) infects CD4+ T cells and gradual depletion ofCD4+ T cells in the blood plasma is the signatureof HIV infection. Traditional models in HIV in-hostinfection considers spread of infection from freeplasma virus to an uninfected CD4+ T cell, knownas cell-free mode of infection. Recent studies, how-ever, confirm that infection can also spread from aninfected cell to an uninfected cell through virolog-ical synapses, known as cell-to-cell mode of infec-tion. Spread of infection and virus replication can beprevented to some extent using retroviral drugs. Inthis paper we consider a HIV multi-pathway infec-tion model with three blockers and study the systemdynamics when these blockers are administered ei-ther individually or in combination. Considering allthree controls as constant, we prove the local as wellas global stabilities of the disease-free and infectedsteady states.

14.3. The space of tree-based phylogeneticnetworksAndrew Francis (Western Sydney University)

13:30 Fri 6 December 2019 – 187

Andrew Francis

Tree-based networks are a class of phylogeneticnetworks that attempt to formally capture whatis meant by “tree-like” evolution. A given non-tree-based phylogenetic network, however, mightappear to be very close to being tree-based, orvery far. This talk will formalise a range of waysto define tree-based proximity for unrooted phy-logenetic networks, one of which (based on the“nearest neighbour interchange (NNI)”) gives riseto a notion of “tree-based rank”. This provides asubclassification within the tree-based networksthemselves, identifying those networks that are“very” tree-based. We also show that the class oftree-based networks as a whole is connected underthe NNI, making it potentially searchable usingNNI for sampling. This is joint work with MareikeFischer, Greifswald Universitat, Germany.

14.4. Extrinsic noise and heavy-tailed distributionsin gene expressionLucy Ham (The University of Melbourne)

13:55 Fri 6 December 2019 – 187

Dr Lucy Ham

Gene expression is an inherently stochastic processresulting in significant heterogeneity between cells;a phenomenon that has been widely observed inexperimental data. The Telegraph model, as intro-duced by Ko et al. in 1991, is the canonical modelfor gene expression, and is commonly invoked asan explanation for this observed heterogeneity. Inthis talk, we present a number of extensions of theTelegraph model, including one that allows us to in-corporate the effects of extrinsic noise, encompass-ing factors external to the transcription of the indi-vidual gene. Crucially, we are able to show that thelarge variability and over-dispersion in the tails seenin many experimental datasets cannot be capturedby the Telegraph model, and must instead reflect ex-trinsic sources of variability.

14.5. Graded rings of Markov invariantstimothy hewson (University of Tasmania)

14:20 Wed 4 December 2019 – 187

Mr timothy john hewson

By considering binary Markov models on phy-logenetic trees and their associated probabilitydistributions, a group action on a tensor prod-uct space is naturally identified together with theassociated graded ring of invariant functions. In

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the case of three taxa and below, these invariantscan be completely accounted for; however at fourtaxa and above the situation becomes much morecomplicated. This talk will review the methodologywe have applied to categorise these functions onhigher number of taxa and give results obtainedthus far.

14.6. Role of induced plant volatile and refuge intritrophic modelDipak Kumar Kesh (Jadavpur University)

14:20 Thu 5 December 2019 – 187

Ritwika Mondal and Dipak Kumar Kesh

Being sessile organism, plant produced volatileplays a major role in plant defense. Plant-induced volatile plays a significant role inplant–herbivore–carnivore interaction. Attrac-tion rate of volatiles influences the immigration rateof carnivores, and hence, predation pressure onherbivores increases. Herbivores take refuge mech-anism to protect themselves from carnivore attacks.Based on such biological phenomena, we haveformulated a tritrophic model of plant–herbivore–carnivore along with herbivore refuge. The modelincludes Holling type II functional responses forherbivores and carnivores. Positivity and bounded-ness of solution of the system, existence of interiorequilibrium and its local stability have been shown.The conditions for the global stability of positiveequilibrium point is derived. Coexistence of all pop-ulations for long time has been studied. Attractionfactor of plants volatile to carnivore and herbivorerefuge, have been considered as sensitive param-eters. Hopf bifurcation has occurred with respectto both of them. The stability of limit cycles duringHopf bifurcation has been studied by computingLyapunov coefficient. Numerical simulations havebeen performed to justify our obtained results.

14.7. Emergent signal processing in T cells viaregulatory immune mechanismsAdarsh Kumbhari (The University of Sydney)

17:15 Wed 4 December 2019 – 187

Adarsh Kumbhari; Peter S. Kim; Peter P. Lee, MD

T-cell expansion is governed by regulatory immunemechanisms. Through simple regulatory modules,T cells perform complex operations involving col-lective decision making and signal processing. Us-ing mathematical modelling, we find that emergentsignal processing by T cells results in a change-detection system, both in response to checkpointand antigen expression. By decomposing the im-mune response into regulatory modules, we pro-vide a framework that may provide insights intomechanisms of immune resistance to checkpoint in-hibitors, and how to optimally modulate immunecheckpoints for combination therapies.

14.8. Pattern formation in a reaction-diffusionpredator-prey-parasite model with prey infectionunder the influence of ecological andepidemiological parametersNandadulal Nandadulal Bairagi (Jadavpur University)

13:55 Thu 5 December 2019 – 187

Prof Nandadulal Nandadulal Bairagi

This paper deals with the spatial pattern forma-tion in a diffusive predator-prey-parasite model,where predator feeds on infected prey followingtype II response function and infection spreadsamong preys through horizontal transmission.We show analytically that diffusion destabilizesthe homogeneous steady-state which is otherwisestable. Criteria for various types of instabilities, likeTuring, Hopf-Turing and pure Hopf, are presentedwith illustrations. Our simulation results revealthat this diffusion-driven instability creates variousspatiotemporal patterns, like spot, stripe, mixture ofspots and stripes, spiral type patterns and clustersdepending upon the values of some ecologicalparameter and diffusion rates. Another interestingobservation is that the epidemiological parametersthat measure the infection rate and virulence of thedisease show opposite patterns with their increasingvalues.

14.9. Modelling the Immune Response of CD4+ Tcells: An intimate relationship between T cells andAPCsPantea Pooladvand (The University of Sydney)

17:40 Wed 4 December 2019 – 187

Ms Pantea Pooladvand, A/Prof Peter Kim

The clonal expansion of T cells during an infectionis a tightly regulated event to ensure an appropriateimmune response is mounted against invadingpathogens. Although experiments have mappedthe dynamics of the response from expansion tocontraction, the mechanisms which control thisresponse are not well defined. Here, we propose amodel in which the dynamics of T cell expansion isultimately controlled through continuous interac-tions between T cells and antigen presenting cells.T cell clonal expansion is proportional to antigenavailability and antigen availability is regulatedthrough downregulation of antigen by T cells. Weshow that our model can predict overall T cellexpansion, recruitment into division and burst sizeper cell. Importantly, the findings demonstrateshow an intimate relationship between T cells andAPCs can explain the ability of the immune systemto tailor its response to dose of antigen, regardlessof initial T cell precursor frequencies.

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14.10. The ancient Operational Code is embeddedin the amino acid substitution matrix and aaRSphylogeniesJulia Shore (University of Tasmania)

14:45 Wed 4 December 2019 – 187

Mrs Julia Shore

Amino-acetyl tRNA synthase (aaRS) are a set of 20enzymes essential in the biological process of geneexpression. For most life forms, they can be di-vided by their chemical properties into two cate-gories: Class I and Class II. Our analysis aimed tofind ways of testing the hypothesis that aaRS en-zymes came into existence at the same time as thegenetic code and had a role in how it was deter-mined.

The methods for this analysis brought about waysof building a family of stochastic rate matrices froma phylogenetic tree which was then fit to empiricaldata. It was found that for a given tree, the set ofMarkov matrices that could be generated formed aclosed set under matrix multiplication and addition.

The results of the analysis found that trees whichtook into account aaRS class fit data better than ran-domly generated trees. Other chemical propertiesof interest, particularly polarity of amino acids, wereused to build trees and it was found that some typesof tree generally fit the data better than ones thatonly took aaRS class into account. However, it wasfound in these cases that also including aaRS classinto the analysis improved the trees even more.

For further analysis, an F-test was developed to com-pare the matrices generated by two nested trees tosee if the fit improvement of their respective ma-trices was statistically significant. This analysis re-sulted in confirming that aaRS class did add signif-icant improvement to trees that took into accountother chemical properties.

14.11. Investigating rank-based approaches forinferring phylogeniesJoshua Stevenson (University of Tasmania)

16:50 Wed 4 December 2019 – 187

Mr Joshua Stevenson

Flattenings are matrices constructed using site-pattern counts from an alignment. These matricesprovide a way of identifying ‘true’ splits, and hencethe true evolutionary tree, via the evaluation of theirrank. The size of these matrices, exponential inthe number of taxa, introduces a computationalchallenge. This challenge led to the developmentof so-called subflattenings (Sumner, 2017), whichexhibit analogous rank properties but have smallerdimensions (quadratic in the number of taxa). Theconstruction of subflattenings involves represen-tation theory and the application of a similaritytransformation in which some choices are involved.

This talk summarises my Honours thesis, which ex-plores some algebraic concepts related to these ma-trices, and the practical implications of some possi-ble choices in the construction of subflattenings.

14.12. The origins of heavy-tailed laws in biologyMichael Stumpf (The University of Melbourne)

13:30 Wed 4 December 2019 – 187

Prof Michael Stumpf

Fat tails and power law distributions have fascinatedresearchers from all disciplines, and have gainedperhaps particular prominence in biology. Here Iwill look at this from a statistical physics perspectiveand discuss representative examples from biologicalnetworks and gene expression models and data. Iwill pay particular attention to different sources ofnoise and how they affect cellular states and our ob-servations of cellular behaviour.

14.13. The Markov embedding problem from analgebraic perspectiveJeremy Sumner (University of Tasmania)

16:00 Wed 4 December 2019 – 187

Jeremy Sumner and Michael Baake

A Markov matrix is said to be embeddable if it admitsa representation as the exponential of a rate (genera-tor) matrix. Equivalently, a Markov matrix is embed-dable if and only if it arises as a probability transitionmatrix for a (finite-state) continuous-time Markovchain. In this work, we revisit the Markov embed-ding problem from an algebraic perspective with afocus on model-specific variants; in particular, wetake examples from nucleotide substitution modelscommonly used in phylogenetics. Algebraically, weshow that the centralizer of the Markov matrix playsa pivotal role in controlling the solution space.

14.14. Symmetry and redundancy: choosing theright algebra for circular genome distancecomputationsVenta Terauds (University of Tasmania)

15:35 Wed 4 December 2019 – 187

Dr Venta Terauds

The maximum likelihood estimate of time elapsed(MLE) has many advantages over other estimatesof evolutionary distance for circular genomes underrearrangement models. However, even when oneutilises the representation theory of the symmetricgroup algebra to convert the combinatorial compu-tations into matrix ones, the calculation of MLEs re-tains a factorial complexity.

We show that the appropriate theoretical setting forthe MLE computations is in fact not the symmetricgroup algebra but a smaller algebra. By incorporat-ing the symmetry of the genomes and the model intothe structure of the algebra, we remove redundancy

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in the calculations and make a commensurate gainin efficiency.

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15. Mathematics Education

15.1. Learning and Teaching in a Digital worldJoshua Capel (UNSW Sydney)

14:45 Wed 4 December 2019 – G60

Dr Joshua Capel

In the 1955 we were told ‘The future is now’ but de-spite this the future still keeps coming.

For a few years now the school of Mathematicsand Statistics at UNSW has been replacing selectclassroom tutorials with so-called ‘Online Tutorials’.These are content delivered through various onlineplatforms like Numbas and MapleTA, and (at firstglance) doesn’t appear to involve a tutor at all.

More recently the school has trying out ‘virtual tu-torials’, which are a more traditional tutorial settingbut attended and participated through video confer-encing software (blackboard collaborate).

In this talk I will discuss some of the challenges wefaced learning and teaching in this brave new digitalworld, as well as some of the benefits and disadvan-tages.

15.2. Empowering, Engaging and EnhancingStudents’ Learning using a Pen-Enabled TabletRenu Choudhary (Auckland University of Technology)

16:25 Wed 4 December 2019 – G60

Dr Renu Choudhary

Using a pen-enabled tablet (PET) to teach Mathe-matics to pre-degree students has evolved my teach-ing process as I have not only been able to com-pletely replace the whiteboard but have also beenable to use physical teaching space flexibly. Un-earthing the multifarious advantages of using PET ininitial years and reflecting on its impact on students’learning has inspired me to explore new tools to fur-ther enhance their experience.

Two years ago, I started using a wireless connectorto project my tablet, and this notably transformedthe classroom dynamic. This allows students to con-tribute to the sessions by writing on the PET from thecomfort of their desk, while it is projected in real-time. In this talk, I will focus on how I used a pen-enabled tablet to empower students, while activelyengaging them with resources and peers to furtherenhance their learning experience. Besides some ofmy reflections, I will share students’ comments andexamples of their work to show the impact that tech-nology can have on communicating mathematicalideas and knowledge.

15.3. Should I apply for a Teaching AwardDiane Donovan (The University of Queensland)

16:50 Wed 4 December 2019 – G60

Prof Diane Donovan

This session will be an open discussion with an op-portunity to ask questions and share ideas with apanel of well known experienced mathematics ed-ucators, including Kumudini Dharmadasa, DeborahKing, Anthony Morphett.

Each panel member will give a brief presentationson how they would structure an application, with aparticular emphasis on evidencing and bench mark-ing.

All members of the AustMS are encouraged to jointhis discussion.

15.4. Blended learning in a large first yearmathematics coursePoh Hillock (The University of Queensland)

13:30 Wed 4 December 2019 – G60

Dr Poh Hillock

The UQ2U program at The University of Queens-land aims to redevelop UQ’s large courses to delivermore flexibility and high value on campus activities.In 2018, MATH1051 (Calculus and Linear AlgebraI), our largest first year mathematics course (yearlyenrolment of 1500) was selected for the UQ2Uprogram. The project has resulted in the devel-opment of online resources delivered through theedge.edx platform, and the subsequent re-designof MATH1051. In this presentation, I describe theUQ2U MATH1051 journey, from the developmentof resources to implementation in Semester 1, 2019and improvements made in Semester 2, 2019. I willshare lessons learned, what worked, what didn’t,and where we go from here!

15.5. Igniting interest, inspiration, investigationand intrigue within mathematics support.Deborah Jackson (La Trobe University)

15:10 Fri 6 December 2019 – G60

Dr Deborah Jackson

Mathematics support centres can have differentfoci, targets and emphases, depending on what typeof support is offered and how they are set up. Suchsupport can simply be used for subject and assign-ment help and guidance. If promoted or managedin this manner, the student will come along withexpectations that they need only solve their currentproblems and look no further. Eking out deep math-ematics anxieties or skills deficiencies is often notpart of a student’s psyche, and many leave furtherlearning to some other time or place, creating adanger of ‘surface learning’. With such a scenario,a support centre can become dull and lifeless atcertain times, and busy, cumbersome, and hectic atothers. However, support centres can be much morethan this. They can • encourage students to confronttheir inadequacies and do something about them,

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• ignite interest in what mathematics is all about,and where it is used, • set out to intrigue studentsand encourage them to investigate, • motivateand inspire students to appreciate the real beautyof mathematics and how it has evolved throughhistory. Support centres that manage to reach outpast the norm become places where students cando more than solve subject specific problems. Theycan engage students in deep learning, discussion,and attention to detail. They can be places forproviding rest and nurturing for the weary, and, atthe same time, inspire the curious and intrigued.This talk discusses how we can make such supporthappen. Within a changing environment, wherestudents need more support than ever, creating afuture where mathematics support is a living andvibrant part of student learning is essential.

15.6. Peer assessment and feedback - in class andonlineSimon James (Deakin University)

13:55 Wed 4 December 2019 – G60

Dr Simon James

Peer feedback has the potential to help engage stu-dents toward higher cognition thinking whether im-plemented in online environments or on-campusclassrooms. I will reflect on my own experiencesin anonymous online peer feedback for problem-solving portfolios as well as discussing what the lit-erature has to say about some other models. Discus-sion and ideas will be welcome!

15.7. Assessment in First Year MathematicsJonathan Kress (University of New South Wales)

13:55 Fri 6 December 2019 – G60

Assoc Prof Jonathan Kress

Recent changes to first year mathematics courses atUNSW will be discussed. Comparable exam ques-tions from before and after the change have beenanalysed with clear evidence of improvement in stu-dent achievement.

15.8. Can Kuhn revolutionise mathematicsteaching?Terence Mills (La Trobe University)

15:35 Fri 6 December 2019 – G60

Terence Mills and Aimé Sacrez

School students might be forgiven for thinking thatonce mathematical ideas are fixed, they are fixed for-ever. Mathematics is right or wrong. Yet, mathe-maticians know that this is not the whole story. In1962 Thomas Kuhn introduced the term ‘paradigmshift’ to the philosophy of science. The purpose ofthis paper is to identify paradigm shifts that have oc-curred in mathematics, and discuss their relevanceto school mathematics. Kuhn’s ideas can be used to

promote awareness that mathematics adapts to dif-ferent cultural-historical contexts. In the words ofthe Australian Curriculum, this will assist students,“to develop an understanding of the relationship be-tween the ‘why’ and the ‘how’ of mathematics”. Thispaper was first presented as a Short Communicationat the 42nd annual conference of the MathematicsEducation Research Group of Australasia.

15.9. Can Comparative Judgement ImproveStudent Performance with Rational Inequalities?Jennifer Palisse (The University of Melbourne)

14:20 Wed 4 December 2019 – G60

Jennifer Palisse

Comparative judgement is a process that has re-cently been used for assessing and ranking studentwork that has been difficult to assess using tradi-tional methods such as rubrics or marking schemes.It involves an assessor being shown two pieces ofwork, from which they had to judge which is best. Bycompleting a large number of judgements, a reliableranking of student work can be obtained. Most re-search on comparative judgement in education hasfocused on whether it can be reliably used as an as-sessment tool for large scale exams, that is, whetheran acceptable level of agreement exists between as-sessors. More recently, comparative judgement hasincluded students as peer-assessors. While, com-parative judgement is receiving increased interestas a learning tool (Jones & Inglis, 2015; Jones &Wheadon, 2015; Potter et al., 2017), very little isstill known about how individuals make their deci-sions or whether the process can offer the assessormeaningful learning benefits. This presentation re-ports early findings from a study on the role com-parative judgement might play in improving stu-dent performance and student understanding. Thestudy involved first year mathematics students whowere given a rational inequalities problem to solve.Early results suggest that the process of comparativejudgement marginally improved the performance ofsome high-ability students but did little to resolvepre-existing misconceptions of low-ability studentswith no improvement in performance.

15.10. Making the Grade: Do Mathematics MarksMatter to Women in STEMJennifer Palisse (The University of Melbourne)

13:30 Fri 6 December 2019 – G60

Deborah King, Jennifer Palisse

The disparity between female and male participa-tion in fields that are underpinned by mathematics,for example, science, engineering and technology,is well known and has been researched for decades.Although significant attention has been focused onredressing this imbalance and programs have beenpurposefully designed to encourage and support

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girls in Science, Technology, Engineering and Math-ematics (STEM), the gender gap persists at all levelsof education and in the workplace.

We discuss preliminary results of a study conductedat a high-ranking Australian university. Participantsof the study were undergraduate students pursuinga major that required tertiary mathematics. The aimof the study was to determine if students’ percep-tions of their mathematics results impacted on theirdecision to continue with their current major.

While students’ satisfaction with grades was linkedto their commitment to their current major for bothmale and female students, differences between gen-ders were found with female students significantlymore sensitive to their perception of performancein the critical first-semester of university than theirmale peers, impacting negatively on their intentionto persist with their major.

15.11. Mathematics Enrichment Program at UNE– from Primary School to UniversityJelena Schmalz (University of New England)

16:00 Wed 4 December 2019 – G60

Dr Jelena Schmalz

At UNE we have started several non-curriculummaths activities during the recent two years, namelya Maths Club for primary school students, a websitewith mathematical puzzles and challenges for highschool students, and a problem solving seminar foruniversity students. In this talk we explain the aimsand reasons for starting these initiatives, describethe activities, and the outcomes.

15.12. Does the Effectiveness of Mathematics andStatistics Support Depend on Students’Mathematical Background?Donald Shearman (Western Sydney University)

14:20 Fri 6 December 2019 – G60

Donald Shearman, Gizem Intepe, Leanne Rylands

Learning support for mathematics and statistics isoffered by most Australian universities. A number ofstudies have shown that there is a positive associa-tion between students’ use of such support and stu-dent success in mathematics and statistics subjects.Relatively little research has been conducted intothe role of confounding variables such as students’mathematical background on this association.

At Western Sydney University mathematics andstatistics support is provided by a centrally organ-ised unit, the Mathematics Education Support Hub(MESH). MESH offers both face-to-face and onlinesupport. The two main face-to-face support servicesare workshops held prior to major assessments forstudents taking first-year mathematics and statisticssubjects; and one-to-one consultation sessions.Data about student use of both of these services iscollected by MESH. We have been able to merge

this data with university records including students’mathematical background, final subject marks anddiscipline.

Analysis of the data suggests that whilst use of sup-port is associated with improved student outcomes,there are significant differences in the extent ofimprovement based on the students’ mathematicalbackground and the mode of support used. Asurprising result of this analysis is the difference inimprovement by students with no senior secondaryschool mathematics compared with those whoundertake elementary level mathematics study intheir final two years of secondary school.

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16.1. Noncommutative Field Theory and DiscreteOrthogonal PolynomialsCiprian Sorin Acatrinei (National Institute for Nuclear

Physics and Engineering)

16:00 Tue 3 December 2019 – G55

Dr Ciprian Sorin Acatrinei

Field theories defined on a non-commutative spaceallow for a natural discretization of their base spaceand consequently of their equations of motion.These involve, for example, Hahn polynomials inthe case of S2 non-commutativity. A study of theproperties of such field theories together with anumber of interesting mathematical questions theyengender will be presented.

16.2. Selberg integrals and the AGT conjectureSeamus Albion (The University of Queensland)

14:20 Wed 4 December 2019 – G55

Mr Seamus Albion

The Selberg integral is an important multidimen-sional analogue of Euler’s beta integral first provedby Selberg in 1944. In their recent verification ofthe AGT conjecture for SU (2), Alba, Fateev, Litvinovand Tarnopolskiy (AFLT) discovered a new generali-sation of Selberg’s integral with a pair of Jack polyno-mials inserted in the integrand. I will discuss a gen-eralisation of the integral of Alba et al. for SU (n), aswell elliptic and q-analogues of the AFLT integral.

16.3. Semi-flexible polymers in a strip withattractive wallsNicholas Beaton (The University of Melbourne)

15:10 Tue 3 December 2019 – G55

Dr Nicholas Beaton

I’ll discuss a model of linear polymers in a two-dimensional strip. The polymers interact with thewalls of the strip via two Boltzmann weights a,b,with an additional weight c which is used to controlhow flexible or stiff the polymers tend to be. This isa simple model of steric stabilisation, the process bywhich polymers can hold colloidal particles in solu-tion. The model can be solved exactly, and we com-pute quantities like the force exerted by a polymeron the walls of the strip.

This is joint work with Jonathon Liu, Leo Li andThomas Wong.

16.4. Escape estimates for SLELaurence Field (Australian National University)

15:10 Fri 6 December 2019 – G55

Dr Laurence Field

The Schramm-Loewner evolution (SLE) is a family ofrandom non-crossing fractal curves that are the scal-ing limits of interfaces in several critical planar mod-els in statistical mechanics, including percolation,the Ising model and the Gaussian free field. Escapeestimates for SLE are uniform bounds on the prob-ability that the curve escapes far from a target pointgiven the curve so far, and can be used to study thespatial decomposition of SLE. I will discuss proofs ofescape estimates for chordal, radial and two-sidedradial SLE in the simple-curve phase using Brownianexcursion measures (joint work with Greg Lawler),and will also mention the new techniques neededto extend the escape estimates into the non-simplephase.

16.5. Further random matrix fermi gas analogiesPeter Forrester (The University of Melbourne)

16:50 Wed 4 December 2019 – G55

Prof Peter Forrester

It’s well known that the the ensemble of GaussianHermitian random matrices known as the GUE hasmany analogies with the quantum mechanical sys-tems of free fermions on a line, confined by an har-monic trap. Less well known is that the correspond-ing d-dimensional fermi system also shares a num-ber of analogies in relation to properties of its onebody density. We will both review known resultsalong these lines, providing new derivations, andidentify extensions of these results.

16.6. A lattice model with the symmetry of thequantum toroidal g l1 algebraAlexandr Garbali (The University of Melbourne)

14:20 Fri 6 December 2019 – G55

Dr Alexandr Garbali

The quantum toroidal g l1 algebra has an excitingrepresentation theory and multiple connections tovarious problems in mathematical physics. An inter-esting direction is the study of the integrable modelon the infinite dimensional Fock representation ofthis algebra. The central object in this model is theR-matrix. I will focus on the problem of calculationof this R-matrix.

16.7. Critical speeding up in dynamical percolationTimothy Garoni (Monash University)

15:35 Fri 6 December 2019 – G55

Assoc Prof Timothy Garoni

We study the integrated autocorrelation time of thesize of the cluster at the origin in critical dynamicalpercolation. We consider trees, high-dimensionaltori, and boxes on the triangular lattice, and in eachcase show that the autocorrelation time is bounded

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above by a strictly sublinear function of the graphsize. It follows that the cluster size at the originin these models exhibits critical speeding-up, andnoise sensitivity. The main tool used in the proofs isa theorem of Schramm and Steif bounding Fouriercoefficients of functions on the discrete hypercubevia properties of certain randomised algorithms.The resulting randomised algorithms may also be ofdirect practical use for Monte Carlo sampling. Thisis joint work with Eren Elci and Andrea Collevecchio.

16.8. Some recent developments in self-avoidingwalksTony Guttmann (The University of Melbourne)

13:30 Wed 4 December 2019 – G55

Prof Tony Guttmann

Continuing my lifelong interest in this topic, I willdiscuss two recent calculations. (i) New scaling laws(joint work with B Duplantier). (ii) The SAW at thetheta point on the hexagonal lattice (joint work withNick Beaton and Iwan Jensen).

16.9. Alignment percolationMark Holmes (The University of Melbourne)

14:20 Tue 3 December 2019 – G55

Assoc Prof Mark Holmes

Perform site percolation with parameter p on the hy-percubic lattice. From each occupied site look in thedirection of the next occupied site, and declare theentire segment between them to be open (or closed)according to some rule (e.g. open independentlywith probability lambda). Is there an infinite clus-ter of interlocking open segments? This is joint withwith Nick Beaton and Geoffrey Grimmett.

16.10. Large complex systems beyond theinstability thresholdJesper Ipsen (The University of Melbourne)

17:40 Wed 4 December 2019 – G55

Jesper Ipsen

More than 40 years ago, Australian ecologist and ap-plied mathematician Robert May asked in a highlyinfluential paper: "Will a large complex system bestable?" Using a fully random linearised model Mayshowed that a generic complex system becomes un-stable when the number of interacting componentsor the strength of the randomness reaches a certainthreshold. However, due to the assumption of lin-earity May’s model cannot say anything about thewhat happens beyond the instability threshold. Inthis talk we will address this regime though a fullyrandom nonlinear model using techniques from thetheory of Gaussian Random Fields and Random Ma-trices.

Based on work with Yan Fyodorov and Sirio Fedeli atKing’s College London.

16.11. Painlev’e VI in Okamoto’s SpaceNalini Joshi (The University of Sydney)

13:55 Thu 5 December 2019 – G55

Viktoria Heu, Nalini Joshi, Milena Radnovic

The sixth Painlevé equation (PVI) is a nonlinear dif-ferential equation with striking mathematical prop-erties. It can be written as

w ′′ = 1

2

(1

w+ 1

w −1+ 1

w − t

)w ′2 −

(1

t+ 1

t −1+ 1

w − t

)w ′

+ w(w −1)(w − t )

t 2(t −1)2

(α+ βt

w2 + γ(t −1)

(w −1)2 + δt (t −1)

(w − t )2

),

where w is a function of t and α, β, γ, δ are param-eters. In this talk, I will present our work on the dy-namical properties of PVI in its space of initial values,called Okamoto’s space.

16.12. Matrix products involving HermitianRandom MatricesMario Kieburg (The University of Melbourne)

17:15 Wed 4 December 2019 – G55

Dr Mario Kieburg

Products of random matrices have been an impor-tant development in the recent years in randommatrix theory. Their applications are versatile andreach from quantum transport in disordered sys-tems to the stability analysis of complex systems andtelecommunications. One open problem has been,how products involving symmetric spaces like Her-mitian matrices have to be dealt with. Recently, Ihave solved this question by modifying the sphericaltransform approach introduced by Harish-Chandraet al. for groups. I will report on this developmentduring my talk.

16.13. Spectral shift function via regulariseddeterminant of higher orderGalina Levitina (University of New South Wales)

16:50 Tue 3 December 2019 – G55

Dr Galina Levitina

The original formula of M.G.Krein expresses spectralshift function for two self-adjoint operators via ap-propriate perturbation determinant. However, thisformula is suitable for differential operators is lowerdimensions only. We prove a formula of spectralshift function via regularised perturbation determi-nant, which is suitable for differential operators inall dimensions. As an example, we consider Diracoperator on Rd .

16.14. On the global stability of Minkowskispacetimes in string theoryMakoto Narita (National Institute of Technology,

Okinawa College)

15:35 Tue 3 December 2019 – G55

Prof Makoto Narita

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We show a theorem of the global nonlinear sta-bility of Minkowski spacetimes in the Einstein-Maxwell-dilaton-axion (EMDA) system. This systemarises from a low energy effective theory in theheterotic superstring theory. The idea of Lindblad-Rodnianski’s weak null condition is used in theproof. The theorem states that the EMDA equationsin wave and Lorentz gauges with asymptoticallyflat initial data satisfying a smallness conditionproduce causally geodesically complete space-times asymptotically approaching to the Minkowskispacetimes.

16.15. The length of self-avoiding walks on thecomplete graphAbrahim Steve Nasrawi (Monash University)

13:55 Wed 4 December 2019 – G55

Abrahim Nasrawi

We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtainthe leading order asymptotics of the mean and vari-ance of the walk length, as the number of verticesgoes to infinity. Central limit theorems for the walklength are also established, in various regimes offugacity. Particular attention is given to sequencesof fugacities that converge to the critical point, andthe effect of the rate of convergence of these fugacitysequences on the limiting walk length is studiedin detail. Physically, this corresponds to studyingthe asymptotic walk length on a general class ofpseudocritical points.

16.16. The tropological vertexBrett Parker (Monash University)

16:25 Tue 3 December 2019 – G55

Dr Brett Parker

I will discuss new symmetries determining the topo-logical vertex of Aganagic, Kelm, Marino and Vafa.This topological vertex can be interpreted as encod-ing Gromov–Witten invariants, which count holo-morphic curves (classical trajectories of strings insome versions of string theory.) We will see howto count these holomorphic using tropical curves,and the new symmetries of the topological vertexwill have simple geometric interpretation in terms oftropical curves. This is joint work with Norm Do.

16.17. Conformal field theory and the non-abelianSU(2) level k chiral spin liquidThomas Quella (The University of Melbourne)

13:55 Fri 6 December 2019 – G55

Dr Thomas Quella

We construct a family of 1D and 2D long-range SU(2)spin models as parent Hamiltonians associated withinfinite dimensional matrix product states that arisefrom simple current correlation functions in SU (2)k

WZW models. It is also explained how the ground

state wave function can be computed explicitly froma symmetrization procedure applied to k indepen-dent copies of SU (2)1 WZW models.

16.18. Recursions on the Moments of RandomMatrix EnsemblesAnas Abdur Rahman (The University of Melbourne)

15:35 Wed 4 December 2019 – G55

Mr Anas Abdur Rahman

Given a random matrix ensemble, one would liketo investigate the moments of its eigenvalue den-sity. Many ensembles have the property that the mo-ments satisfy recursions, allowing for efficient com-putation. In this talk, I will introduce the aforemen-tioned quantities and then outline two types of mo-ment recursions that I’m currently interested in. Thefirst is derived through the loop equation formal-ism which is related to topological recursion, andthe latter is derived through Selberg correlation in-tegrals and is comparable to the Harer-Zagier recur-sion. Particular attention will be given to the differ-ences between the two types of recursions.

16.19. Quantum Entanglement, Schrodinger’s cat,and the Q-function phase-space model of realityMargaret Reid (Swinburne University of Technology)

13:30 Fri 6 December 2019 – G55

Prof Margaret Reid

In 1935, Einstein, Podolsky and Rosen (EPR) pre-sented an argument for the completion of quantummechanics. Their argument was based on the cor-relation properties of two spin ½ particles preparedin a singlet state. Such a state is said to be ‘entan-gled’. Here, we first briefly outline the features ofthe EPR entangled states, explaining how this ulti-mately lead to Bell’s theorem, which gave proof ofthe incompatibility between all classical local hid-den variable theories and quantum mechanics, andto applications in the field of quantum information.Closely linked with EPR’s argument is the paradox ofSchrodinger’s cat. In quantum theory, when a mea-surement is made, a macroscopic system interactswith a smaller quantum system to create an entan-gled state. The resulting ‘Schrodinger cat-state’ isa superposition of two macroscopically distinguish-able states. The cat-state is apparently paradoxicalbecause according to the standard interpretation ofquantum mechanics, such a system cannot be re-garded as being ‘in one state or the other’, prior toa measurement. We discuss the interpretation of themacroscopic Schrodinger cat-state and of the quan-tum measurement of a qubit system. Using an el-ement of reality approach, we justify that the “col-lapse” of the state of the system to give one or otheroutcome occurs as a result of the amplification as-sociated with the coupling to the macroscopic sys-tem, regardless of decoherence. We then explain

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how one might falsify macroscopic local realism, us-ing Bell inequalities for macroscopic qubits. Thismotivates us to introduce a model of reality basedon the phase space representation known as the Qfunction. In this picture, a physical universe existsin space-time without observers. The measurementis described by dynamical evolution where sharpeigenvalues emerge for sufficient amplification. Weshow how the model is not inconsistent with Bell’stheorem, because of the backwards in time causa-tion which occurs in Q-function dynamics throughnegative diffusion terms.

16.20. On the asymptotic distribution of roots ofthe generalised Hermite polynomialsPieter Roffelsen (International School for Advanced

Studies (SISSA))

14:20 Thu 5 December 2019 – G55

Davide Masoero, Pieter Roffelsen

The generalised Hermite polynomials Hm,n , m,n ∈N, form a family of polynomials with applicationsto random matrices, quantum mechanics and non-linear wave equations. Central in each of these ap-plications is the fact that these polynomials gener-ate rational solutions of the fourth Painlevé equa-tion. About fifteen years ago, Peter Clarkson pub-lished numerical investigations on the distributionsof their roots in the complex plane and posed theproblem of giving an analytic explanation of his nu-merical findings.

In this talk, I will show how the roots of gener-alised Hermite polynomials can be characterised interms of an inverse monodromy problem concern-ing a class of anharmonic oscillators. A complexWKB approach to latter oscillators yields a uniform,asymptotic description of the bulk of the roots interms of elliptic integrals as the degree deg(Hm,n) =m × n grows large. The roots, after proper rescal-ing, densely fill up a bounded quadrilateral regionin the complex plane and, within this region, organ-ise themselves along a deformed rectangular lattice,yielding an asymptotic answer to Clarkson’s prob-lem.

This talk is based on two joint papers with DavideMasoero:-Roots of generalised Hermite polynomials whenboth parameters are large, ArXiv, 2019;-Poles of Painlevé IV Rationals and their Distribu-tion, SIGMA, 2018.

16.21. Rolling, rolling, rollingKatherine Anne Seaton (La Trobe University)

14:45 Wed 4 December 2019 – G55

Dr Katherine Anne Seaton

In this talk I will describe some results from an ongo-ing collaboration with an inventor. The constructionand the features of intriguing ‘new’ solids (devisedby David Hirsch) will be outlined. These solids roll

in an amusing fashion, and are both mathematicalart (kinetic sculptures) and mathematical physics.

16.22. Hierarchies of q-discrete second, third andfourth Painlevé equations and their propertiesDinh Tran (The University of Sydney)

13:30 Thu 5 December 2019 – G55

Ms Dinh Tran

In this presentation, we give hierarchies ofq-discrete second, third and fourth Painlevé(qPII, qPIII, qPIV) equations. These hierarchies werederived by using geometric reductions/ staircasereductions of a multi-parametric integrable latticeequation. Their Lax pairs can be obtained directlyfrom the staircase reductions.

We then present a method to obtain Bäcklund trans-formations of the hierarchies systematically. Thekey ingredients for this method are the consistencyaround the cube property and the staircase reduc-tions. We are able to recreate the known Bäcklundtransformations for the first member of the qPI I hi-erarchy. Special q-rational solutions of the hierar-chies are constructed and corresponding functionsthat solve the associated linear problems are de-rived.

We also study the symmetry groups of the hierar-chies by using the geometric reductions.

This is joint work with H. D. Alrashdi and N. Joshi.

16.23. Finite size corrections at the hard edge forthe Laguerre β ensembleAllan Trinh (The University of Melbourne)

16:00 Wed 4 December 2019 – G55

Mr Allan Trinh

Universal laws of spectral statistics are central torandom matrix theory. In addition to quantifyingthese laws in large N limit, there is a recent interestin establishing the optimal rate of convergence. Inthis talk, I’ll introduce the classical Laguerre UnitaryEnsemble and its β analogue. Asymptotic results upto the next finite N correction for the distribution ofthe smallest eigenvalue and the spectrum at the socalled hard edge will be discussed.

16.24. Spherical transform and randomised HornproblemJiyuan Zhang (The University of Melbourne)

16:25 Wed 4 December 2019 – G55

Mr Jiyuan Zhang

The randomised Horn problem is to ask for theeigenvalue distribution of sum/product of tworandom matrices. Its simpliest analogue is sumof independent real random variables, which canbe solved using univaraite Fourier transform. Thegeneralisation from real variables to matrices re-quires us to specialise the well-established theory of

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spherical transform to spaces of random matrices.We will introduce spherical transforms for Herm(n),Herm+(n) and U(n), as well as their applications torandomised Horn problems on those spaces. Closedform expressions for the eigenvalue distributionsare given, when one of the two random matrices hasrank 1.

16.25. The coupling time of the Ising GlauberdynamicsZongzheng Zhou (Monash University)

16:00 Fri 6 December 2019 – G55

Dr Zongzheng Zhou

Consider an ergodic Markov chain with n states. Runn chains simultaneously with distinct initial statesbut using the same randomness. There exists a non-negative random variable Tn such that starting at−Tn the n chains will all have coalesced by time0. It was proved by Propp and Wilson that sam-pling at time 0 is exactly stationary. This proce-dure is called "coupling from the past", and Tn iscalled the coupling time. In this talk, we will dis-cuss a limit theorem for the distribution of the cou-pling time of a specific Markov chain: Glauber dy-namics of the Ising model on d-dimensional tori.The infinite temperature case simply corresponds tothe coupon collecting problem, for which Erdos andRényi proved the standardised coupling time con-verges to a Gumbel distribution. In our work, weprove that a similar limit theorem holds down to a fi-nite temperature.The proof relies on the compoundPoisson approximation and the information perco-lation method.

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17. Number Theory and Algebraic Geometry

17.1. Improvements to Dirichlet’s theorem inDiophantine approximationAyreena Bakhtawar (La Trobe University)

16:25 Wed 4 December 2019 – G57

Miss Ayreena Bakhtawar

The starting point of the theory of Diophantineapproximation is Dirichlet’s theorem (1842) whichstudies the approximation properties of real num-bers by rationals with the bounded denominators.In this talk, I will discuss some recent measure the-oretic results regarding improvements to Dirichlet’stheorem.

17.2. Explicit Pólya-Vinogradov for primitivecharacters and large moduliMatteo Bordignon (University of New South Wales

Canberra)

16:25 Tue 3 December 2019 – G57

Mr Matteo Bordignon

We obtain a new fully explicit constant for thePólya-Vinogradov inequality for Primitive charac-ters. Given a primitive character χ modulus q , weprove the following upper bound∣∣∣∣∣ ∑

1≤n≤Nχ(n)

∣∣∣∣∣≤ cp

q log q,

where c = 3/(4π2) + oq (1) for even characters andc = 3/(8π)+oq (1) for odd characters, with an explicitoq (1) term. This improves a result of Frolenkov andSoundararajan for large q . We proceed, following thetrace of a paper by Hildebrand, obtaining the explicitversion of a result by Montgomery–Vaughan on Par-tial Gaussian sums and an explicit Burgess like re-sult on convoluted Dirichlet characters, that simpli-fies Hildebrand’s approach.

17.3. The etale fundamental group of semiringsJames Borger (Australian National University)

13:30 Thu 5 December 2019 – G57

Dr James Borger

Grothendieck extended Galois theory from fields torings in his theory of the etale fundamental group.In this talk, I’ll explain how to extend this to semir-ings, as developed in Robert Culling’s 2019 ANU PhDthesis. I’ll also present his proof that the semir-ing of non-negative reals has trivial fundamentalgroup, much as the complex numbers do (the fun-damental theorem of algebra) and the integers do(Minkowski’s theorem).

17.4. Explicit results on the sum of a divisorfunctionMichaela Cully-Hugill (University of New South Wales

Canberra)

15:35 Wed 4 December 2019 – G57

Ms Michaela Cully-Hugill

We present an explicit bound on the partial sums ofthe divisor function, and areas where this result canbe applied. An intermediate result concerning a dif-ferent divisor function will also be given, as it im-plies a bound on the class number for quartic num-ber fields. This is joint work with Tim Trudgian.

17.5. Burgess’ Bound and kth Power Non-residuesForrest James Francis (Australian Defence Force

Academy)

15:35 Tue 3 December 2019 – G57

Mr Forrest James Francis

Let χ be a Dirichlet character modulo a prime p.Often, one requires estimates for "short" sums overthis character. In this talk, we consider explicit ver-sions of one of these estimates, a family as boundsreferred to as the Burgess’ bound. We’ll look at somesmall improvements to the explicit constant in thisbound, and their application to a problem involvingkth power non-residues modulo p.

17.6. Lower order terms for the one level density ofquadratic Hecke L-functions in the Gaussian fieldPeng Gao (Beihang University)

13:30 Wed 4 December 2019 – G57

Prof Peng Gao

As the density conjecture of Katz and Sarnak relatesthe main term behavior of the n-level density of low-lying zeros of families of L-functions to random ma-trix theory, one can do more on the number theoryside by computing the lower order terms of these n-level densities, which serve to provide us better un-derstandings on the n-level densities. In this talk,we will present a result on the lower order terms ofthe 1-level density of low-lying zeros of quadraticHecke L-functions in the Gaussian field. Assum-ing the Generalized Riemann Hypothesis, we obtainthe lower order terms for even test functions whoseFourier transforms are being supported in (−2,2).This is joint work with L. Zhao.

17.7. Biases, oscillations, and first sign changes inarithmetic functionsShehzad Shabbirbhai Hathi (UNSW Canberra)

16:00 Wed 4 December 2019 – G57

Mr Shehzad Shabbirbhai Hathi

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We will introduce the topic using Skewes’ number:an upper bound for the first sign change of the func-tion π(x) − Li(x). Similar questions can be askedin the case of other arithmetic functions like theMöbius function (and the closely related Liouvillefunction). To this end, we will discuss the Mertensconjecture. While the conjecture implies the Rie-mann Hypothesis, it has been disproved. However,an explicit counterexample to the Mertens conjec-ture still eludes us. We will discuss the scope for im-provement in the existing results.

17.8. On the zero-free region for the Dedekindzeta-functionEthan Simpson Lee (UNSW Canberra)

17:15 Tue 3 December 2019 – G57

Mr Ethan Simpson Lee

Everyone knows and loves the Riemann zeta-function because of its connection to the distri-bution of prime numbers via the prime numbertheorem (1896). For analogous reasons, one shouldalso appreciate the Dedekind zeta-function for itsconnection to the distribution of prime ideals viathe Chebotarëv density theorem (1926). Therefore,we will study the Dedekind zeta-function in thistalk.

17.9. The prime ideal theorem in noncommutativearithmeticSean Lynch (UNSW Sydney)

15:10 Tue 3 December 2019 – G57

A/Prof Daniel Chan & Mr Sean Lynch

An arithmetic order is a noncommutative analogueof the integers. In the early 1980s, Colin J. Bush-nell and Irving Reiner published several papers onL-functions for arithmetic orders and used them tostudy the asymptotic behaviour of associated count-ing functions. Here we focus on the distribution ofmaximal left ideals in arithmetic orders. In particu-lar, we present a method which yields an error termwithout directly appealing to L-functions.

17.10. Quartic Gauss sums and twisted reciprocityBenjamin Moore (The University of Adelaide)

14:20 Wed 4 December 2019 – G57

Mr Benjamin Moore

In 1850, Mathias Schaar discovered an analytic proofof quadratic reciprocity. His proof involved, as anintermediate step, a remarkable identity betweenobjects now known as Gauss sums. This identitywas rediscovered by Landsberg in 1893 and is nowknown as the Landsberg-Schaar relation. Later re-search on Gauss sums focussed on evaluating morecomplicated Gauss sums than the quadratic onesappearing in the Landsberg-Schaar relation, but acomplete solution is known only in the quartic case.We demonstrate that the quartic Gauss sums arise

as a special case of twisted quadratic Gauss sums,and exploit this fact to prove an analogue of theLandsberg-Schaar relation for quartic Gauss sums.

17.11. A combinatoric proof of Jackson’ssummationThomas Morrill (UNSW Canberra)

13:55 Thu 5 December 2019 – G57

Dr Thomas Morrill

Overpartitions are a generalisation of integer par-titions, developed that their combinatorics alignnicely with the coefficients of q-hypergeometricseries. Thus, weight-preserving bijections betweenoverpartitions and related objects are sufficient toprove equality for their associated generating func-tions. Conversely, known series transformationssuggest the existence of such bijections. We focus onthe q-analog of Jackson’s classical 6F5 summationviewed through the lens of overpartition tuples anddiscuss implications for the theory of overpartitionranks.

17.12. On Selberg’s zero density estimate andrelated resultsAleksander Simonic (University of New South Wales

Canberra)

16:50 Tue 3 December 2019 – G57

Mr Aleksander Simonic

Bounds on N (σ,T ), where N (σ,T ) denotes thenumber of zeros ρ = β+ iγ of the Riemann zeta-function ζ(s) with β > σ and γ ∈ (0,T ], are knownas zero density estimates. Explicit results of suchkind are valuable in studying distribution of primenumbers. Recently, there have appeared ex-plicit versions of classical zero density estimates

N (σ,T ) ¿ T and N (σ,T ) ¿ T38 (1−σ) log5 T . In

this talk we will present explicit Selberg’s estimate

N (σ,T ) ¿ T 1− 14

(σ− 1

2

)logT , while related results,

e.g., the second and the fourth power moments ofζ( 1

2 + it), will also be discussed.

17.13. When primes are just too hard. . .Timothy Trudgian (UNSW Canberra)

16:00 Tue 3 December 2019 – G57

Dr Timothy Trudgian

. . . turn to square-free numbers! These include allprimes and those numbers indivisible by squaresof primes (e.g., 6, 10, 14, 15,. . . ) and so are not‘too composite’. If problems involving primes aretoo hard then we must content ourselves with thesquare-frees: the crumbs from the table. I shall out-line the state of play with square-free numbers andsome recent work with Tomás Oliveira e Silva andMike Mossinghoff.

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17.14. Involutive property and irreducibility oftheta correspondenceChenyan Wu (The University of Melbourne)

14:20 Thu 5 December 2019 – G57

Dr Chenyan Wu

Theta correspondence plays a key role in the studyof automorphic forms. We will give a brief introduc-tion of the construction and derive some key proper-ties of theta correspondence of unitary dual reduc-tive pairs, such as an involutive property and irre-ducibility of first occurrence.

17.15. A relaxation of Goldbach’s conjectureKam Hung Yau (University of New South Wales)

14:45 Wed 4 December 2019 – G57

Mr Kam Hung Yau

The Goldbach conjecture states that all even integergreater than two is a sum of two primes. Currentlywe do not have sufficient tools to prove this con-jecture but we can obtain the following relaxation:Uniformly for small q , we obtain an estimate for theweighted number of ways a sufficiently large integercan be represented as the sum of a prime congru-ent to a modulo q and a square-free integer. Ourmethod is based on the notion of local model de-veloped by O. Ramaré and may be viewed as an ab-stract circle method. I will take about the history ofthe problem and an outline of the proof.

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18.1. Zero Duality Gap via Abstract ConvexityThi Hoa Bui (Federation University Australia)

15:10 Tue 3 December 2019 – 188

Ms Thi Hoa Bui

Every convex lower semicontinuous function is theupper envelope of a set of affine functions. Hence,in classical convex analysis, affine functions act as“building blocks” or a family “simpler functions”.The central idea of abstract convexity approach isto replace this family of simpler functions (the lin-ear and affine functions in classical convex analysis),by a different set of functions. These sets are calledabstract linear, and abstract affine sets. Mimickingthe classical setting, abstract convex functions arethe upper envelopes of elements of a set of abstractaffine functions.

By using this approach, we establish conditions forzero duality gap to the context of nonconvex andnonsmooth optimization using tools provided bythe theory of abstract convexity.

18.2. Projection algorithms in wavelet constructionas a feasibility problemNeil Kristofer Dizon (The University of Newcastle)

16:25 Tue 3 December 2019 – 188

Mr Neil Kristofer Dizon

The construction of compactly supported andsmooth multidimensional wavelets with orthogo-nal shifts and multiresolution structure has beenrecently recast as a many-set feasibility problem.The Douglas-Rachford method, together with otherprojection algorithms and their many-set exten-sions, has been successfully employed to solve thisproblem.

In this talk, we report numerical results on circum-centering reflection methods applied to the noncon-vex feasibility problem of wavelet construction. Pe-culiar to the structure of constraints in this problem,we also introduce a constraint reduction reformula-tion for well-known projection algorithms to accel-erate convergence.

18.3. A Progressive Hedging - Feasibility Pump forStochastic Integer ProgrammingAndrew Craig Eberhard (RMIT University)

15:10 Fri 6 December 2019 – 188

Prof Andrew Craig Eberhard

Stochastic mixed-integer programming (SMIP)models are, in essence, large-scale mixed-integerprogramming (MIP) models in which the uncer-tain nature of the input parameters are modelledby means of discrete scenarios. The strategy ofsolving deterministic equivalents of SMIP modelsoften proves to be unfruitful, since it encompasses

converting into very large-scale MIP counterparts.A much more promising strategy consists of ex-ploiting the particular structure that SMIPs presentto develop specialised solution methods that canimplicitly cope with their large-scale nature. Recentdevelopments stemming from the employmentof Lagrangian decomposition for SMIP have rep-resented an important step towards developingspecialised B&B methods for SMIP.

In this talk, we turn our focus to another impor-tant component for a B&B approach, in particular,methods that can generate feasible solutions andhence improve primal (upper) bounds. There area number of fields in discrete optimisation wherethere have been developed heuristics that are mo-tivated by ideas from feasibility methods. The mostnotable example is the “Feasibility Pump” used forfinding good feasible solutions of a Mixed IntegerLinear Program (MIP). This is a general method thatdoes not exploit the special structure of SMIP andso suffers from the same problems of dimensional-ity as the deterministic equivalent. We will discussa modified version of a penalty-based Gauss-Seidelmethod commonly used in stochastic programmingthat has strong theoretical properties for certain im-portant sub-classes of Stochastic Integer Programs(SIP). In particular we will show that the modified al-gorithm avoids the pitfall associated with the largescale equivalent problem and always converges toa feasible point. Some computational experimentswill also be presented.

18.4. Linear Programming Based OptimalityConditions for Long Run Average Optimal ControlProblemsVladimir Gaitsgory (Macquarie University)

14:20 Fri 6 December 2019 – 188

Prof Vladimir Gaitsgory

We will consider an infinite time horizon optimalcontrol problem with time discounting and time av-eraging criteria. We will state results establishingthat the Abel and Cesaro limits of the optimal valueare bounded from above by the optimal value ofa certain infinite-dimensional linear programming(IDLP) problem and that these limits are boundedfrom below by the optimal value of the correspond-ing dual IDLP problem. Using this fact and as-suming that there is no duality gap, we will estab-lish sufficient and necessary optimality conditionsfor the long-run-average optimal control problem inthe general case when the limit optimal value maydepend on initial conditions of the system. The talkis based on results obtained in collaboration with V.Borkar and I. Shvartsman.

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18.5. On the strong minimum in optimal control.A view from variational analysis.Alexander Ioffe (Technion, Israel Institute of

Technology)

13:30 Fri 6 December 2019 – 188

Prof Alexander Ioffe

Among applications of variational analysis (andmetric regularity theory in particular) to optimiza-tion one of the most important is connected withthe possibility to equivalently reduce constrainedproblems to unconstrained minimization of suffi-ciently well organized functionals. It opens doorsto a fairly new approach to the study of necessaryoptimality conditions that allows to substantiallyshorten and simplify proofs of known results and toget new results not detected earlier by traditionalvariational techniques.

In optimal control the unconstrained problem hasa form of a Bolza problem of calculus of variationswith, necessarily, nonsmooth integrand and off-integral term. In the talk I shall briefly describehow this approach works for a proof of the Pon-tryagin maximum principle and then tell about anew second order necessary condition for a strongminimum (which in particular implies a totally newsecond order condition for a strong minimum in theclassical problem of calculus of variations). If timepermits, I shall show that the new conditions maywork when the known necessary conditions fail.

18.6. About the Radius of Metric SubregularityAlexander Kruger (Federation University Australia)

14:20 Tue 3 December 2019 – 188

Asen L. Dontchev, Helmut Gfrerer, Alexander Y. Kruger,

Jirí V. Outrata

There is a basic paradigm, called the radius of well-posedness, which quantifies the “distance” from agiven well-posed problem to the set of ill-posedproblems of the same kind. In variational analy-sis, well-posedness is often understood as a regu-larity property, which is usually employed to mea-sure the effect of perturbations and approximationsof a problem on its solutions. We focus on evaluat-ing the radius of the property of metric subregularitywhich, in contrast to its siblings, metric regularity,strong regularity and strong subregularity, exhibits amore complicated behaviour under various pertur-bations. We consider three kinds of perturbations:by Lipschitz continuous functions, by semismoothfunctions, and by smooth functions, obtaining dif-ferent expressions/bounds for the radius of subreg-ularity, which involve generalized derivatives of set-valued mappings.

The research was supported by the Australian Re-search Council, project DP160100854

18.7. On the Projected Polar Proximal PointAlgorithmScott Boivin Lindstrom (Hong Kong Polytechnic

University)

14:20 Thu 5 December 2019 – 188

Dr Scott Boivin Lindstrom

The Projected Polar Proximal Point Algorithm wasrecently introduced by M.P. Friedlander, I. Macedo,and T.K. Pong for solving convex optimization prob-lems through gauge duality. We introduce the basicconcepts and provide answers to several open ques-tions about its convergence properties. In particular,we characterize its set of fixed points, and we provestrong convergence to a fixed point.

18.8. Minimizing Control Volatility for NonlinearSystems with Smooth Input SignalsRyan Loxton (Curtin University)

16:50 Tue 3 December 2019 – 188

Prof Ryan Loxton

We consider a class of nonlinear optimal controlproblems in which the aim is to minimize controlvariation subject to an upper bound on the sys-tem cost. This idea of sacrificing some cost in ex-change for less control volatility, thereby making thecontrol signal easier and safer to implement, is ex-plored in only a handful of papers in the literature,and then mainly for piecewise-constant (discontin-uous) controls. In this talk, we consider the case ofsmooth continuously differentiable controls, whichare more suitable in several applications, includingrobotics and motion control. In general, the controlsignal’s total variation, which is the objective to beminimized in the optimal control problem, cannotbe expressed in closed-form. Thus, we introduce asmooth piecewise-quadratic discretization schemeand derive an analytical expression, which turnsout to be rational and non-smooth, for computingthe total variation of the approximate piecewise-quadratic control. This leads to a non-smooth dy-namic optimization problem in which the decisionvariables are the knot points and shape parame-ters for the approximate control. We then presentresults showing that this non-smooth problem canbe transformed into an equivalent smooth problem,which is readily solvable using standard optimiza-tion techniques.

18.9. Strong Valid Inequalities Identification forMixed Integer Programs with a given Set ofSolutionsAsghar Moeini (Curtin University)

15:35 Tue 3 December 2019 – 188

Dr Asghar Moeini

The characterization of strong valid inequalities forinteger and mixed-integer programs is more of an

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18. Optimisation

artistic task than a systematic methodology, requir-ing inspiration that can sometimes be elusive. Fre-quently, this task is facilitated by somehow exploit-ing the structure of problems for devising strongvalid inequalities. Subsequently, various mathemat-ical techniques are utilized for proving that those in-equalities, which are often easily shown to be valid,are indeed strong in the sense that they representfacets or other high dimensional faces. This paperdevelops a method to assist modelers in the chal-lenge to devise strong valid inequalities. In eachiteration, the proposed algorithm generates a validinequality by solving a suitably constructed linearmixed integer program and applies some quality cri-teria in order to determine if it is a new strong validinequality. To illustrate the proposed algorithm, anew Traveling Salesman Problem (TSP) formulationis developed based on a set of constraints alreadyconstructed in the context of the Hamiltonian CycleProblem (HCP), and then the proposed algorithmis employed to derive a set of strong inequalities totighten this TSP formulation. Finally, a comparisonstudy between the relaxation of the new TSP formu-lation and that of a state-of-the-art TSP formulationis conducted. The computational study confirms theeffectiveness of the devised inequalities due to thebetter quality of the relaxation provided by the newformulation.

18.10. Characterizations of Robinson regularityproperties of implicit multifunctions andapplicationsCuong Nguyen Duy (Federation University Australia)

16:00 Tue 3 December 2019 – 188

Nguyen Duy Cuong, Alexander Kruger

In this talk, we discuss primal and dual sufficientconditions for Robinson regularity properties of im-plicit multifunctions in normed (in particular, Ba-nach/Asplund) spaces. These results are presentedin terms of slopes and Clarke/Fréchet subdiffer-entials and normals. These types of conditionsare often overlooked depsite appearing implicitly inproofs of many satements in the literature. We makean attempt to present the conditions explicitly. In-terestingly, we prove that these conditions becomenecessary for the properties in the convex setting.As applications, we establish primal and dual char-acterizations of the conventional metric regularityproperties of set-valued mappings as well as stabilityproperties of a solution mapping of a semi-infinitemultiobjective optimization problem.

18.11. A linear programming approach toapproximating the infinite time reachable set ofstrictly stable linear control systemsJanosch Rieger (Monash University)

15:35 Fri 6 December 2019 – 188

Prof Andreas Ernst, Prof Lars Grüne, Dr Janosch Rieger

We develop a new numerical method for approxi-mating the infinite time reachable set of strictly sta-ble linear control systems. By solving a linear pro-gram with constraints that incorporate the systemdynamics, we compute a polytope with fixed facetnormals as an outer approximation of the limit set.In particular, this approach does not rely on forwarditeration of finite-time reachable sets.

18.12. Optimal selling mechanism design in thepresence of budget constraintsVera Roshchina (UNSW Sydney)

16:25 Fri 6 December 2019 – 188

Dr Vera Roshchina

A seller would like to sell a range of goods in a way tomaximise revenue. Each buyer has a type encodedby a valuation function and a budget constraint. Theseller only knows the buyers’ types and their (proba-bility) distribution.

We focus on the discrete setting where the numbersof goods and buyers are finite. An optimisation for-mulation of this problem happens to have a discon-tinuous objective, linear on non-convex regions withtropical boundary. The structure of the problem al-lows for the design of an algorithm that solves it tooptimality, however we are only able to resolve verysmall instances due to combinatorially inefficientenumeration step.

I will give a brief overview of the problem fromthe economics perspective, describe the structure ofthe optimisation formulation, explain our algorithmand the challenges that so far prevented us from de-signing a more efficient solution. It would be inter-esting to figure out the true complexity of this prob-lem, and to see if there is a way to improve the effi-ciency of the numerical approach.

This talk is based on collaborative work with SabrinaDeo and Juan Carlos Carbajal (both at UNSW Syd-ney).

18.13. Certifying polynomial nonnegativity viahyperbolic optimisationJames Saunderson (Monash University)

13:55 Thu 5 December 2019 – 188

Dr James Saunderson

A key connection between real algebraic geomet-ric and optimisation is that we can check whethera multivariate polynomial is a sum of squares bysolving a semidefinite optimisation problem. Thistalk will focus on an alternative approach to certi-fying the nonnegativity of homogeneous multivari-ate polynomials that is based on the theory of hy-perbolic polynomials, and can be made effective bysolving hyperbolic optimisation problems. I will in-troduce this approach and discuss known relation-ships between these hyperbolic certificates of non-negativity and sums of squares. On the way, I’ll

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touch on why it is NP-hard to decide hyperbolicityof cubics, and exhibit the first explicit example of ahyperbolic cubic for which no power has a definitedeterminantal representation.

18.14. Remez method applicability in Chebyshevapproximation problemsNadia Sukhorukova (Swinburne University of

Technology)

13:30 Thu 5 December 2019 – 188

Dr Nadia Sukhorukova

In this presentation I will talk about the applicationof Remez algorithm, originally designed for polyno-mial approximation, to a wider class of problems.Some of these problems can be considered as nat-ural extensions of the classical polynomial approxi-mations, while some others are application driven.One application area is signal clustering and signalprocessing.

18.15. Stochastic Variational Inequalities, NashEquilibria under Uncertainty, and the ProgressiveHedging AlgorithmJie Sun (Curtin University)

17:15 Tue 3 December 2019 – 188

Prof Jie Sun

The concept of a stochastic variational inequal-ity has recently been extended to a format thatcovers, in particular, the optimality conditionsfor multistage stochastic programming and Nashequilibrium problems. This extension may havegreat impact on solving stochastic optimization andequilibrium problems. One of the long-standingmethods for solving such optimisation problems isthe progressive hedging algorithm. That approachis demonstrated here to be applicable also to solv-ing multistage stochastic variational inequalityproblems under monotonicity. Stochastic com-plementarity problems are presented as a specialcase and explored numerically in a linear two-stageformulation.

18.16. Best chebyshev approximation by rationalfunctionsJulien Ugon (Deakin University)

16:00 Fri 6 December 2019 – 188

Dr Julien Ugon

In this presentation we will review some results onapproximation by rational functions. We will pro-vide an alternation theorem, and show how this typeof approximation fits within a more general Cheby-shev approximation framework.

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19.1. Limit theorems for filtered long-rangedependent random fieldsTareq Alodat (La Trobe University)

17:15 Wed 4 December 2019 – 183

Mr Tareq alodat

We investigate general scaling settings and limit dis-tributions of functionals of filtered random fields.The filters are defined by the convolution of non-random kernels with functions of Gaussian randomfields. The case of long-range dependent fields andincreasing observation windows is studied. The ob-tained limit random processes are non-Gaussian.Most known results on this topic give asymptoticprocesses that always exhibit non-negative auto-correlation structures and have the self-similar pa-rameter H ∈ (0.5,1). In this work we also obtainconvergence for the case H ∈ (0,0.5) and show howthe Hurst parameter H can depend on the shape ofthe observation windows. Various examples are pre-sented.

19.2. Yaglom Limit for Stochastic Fluid ModelsNigel Bean (The University of Adelaide)

15:35 Fri 6 December 2019 – 183

Prof Nigel Bean

In this paper we provide the analysis of the limitingconditional distribution (Yaglom limit) for stochas-tic fluid models (SFMs), a key class of models in thetheory of matrix-analytic methods. So far, transientand stationary analysis of SFMs only has been con-sidered in the literature, while limiting conditionaldistributions are only known for a limited class ofstochastic models.

The crucial idea is to show equivalence of a singu-larity of a key matrix in SFM theory with the inter-section of the spectra of two other key matrices. Wethen exploit the Heaviside principle to deduce theform of the limiting conditional distribution.

In this talk I’ll show the audience some highlights ofthis journey.

19.3. Novel Methods for Model Selection in LinearRegressionZdravko Botev (University of New South Wales)

13:55 Wed 4 December 2019 – 183

Dr Zdravko Botev

In this talk we explain how lasso-type model selec-tion methods can sometimes fail using a few simplestylistic examples. Using Bayesian ideas of regular-ization, we suggest a simple remedy that, at least inthe examples we tested, significantly improved theidentification of the correct model.

19.4. Strongly Vertex-Reinforced Jump Processeslocalizes on 3 pointsAndrea Collevecchio (Monash University)

17:15 Tue 3 December 2019 – 183

Dr Andrea Collevecchio

We study Vertex-Reinforced Jump Processes on theline. We prove that under strong reinforcement, theprocess localizes on exactly 3 points.

19.5. On some asymptotics of functionals oflong-range dependent random fields.Illia Donhauzer (La Trobe University)

16:50 Wed 4 December 2019 – 183

Mr Illia Donhauzer

We will discuss random fields possessing long-rangedependence. We consider nonlinear integral func-tionals of the homogeneous isotropic Gaussian ran-dom field with long-range dependence∫

∆(r t1n )

Hm(ξ(x))d x,r →∞where Hm is a Hermite polynomial of rank m, ξ(x)is a long-range dependent homogeneous isotropicGaussian random field and ∆ ∈ Rn is an observationwindow, ∆(r t

1n ) is a homothetic image of ∆ with a

coefficient r t1n .

Limits of these functionals are random processesrepresented by the Wiener-Ito integrals. Limit pro-cesses have different properties depending on thegeometrical properties of the observation window ∆

and its dimensionality n. It is known that in the one-dimensional case, the limit processes have the prop-erty of the stationarity of increments for all obser-vation windows ∆. We study properties of the limitprocesses depending on the observation windows ∆in the multidimensional case.

19.6. Local Brownian MotionsJie Yen Fan (Monash University)

15:35 Wed 4 December 2019 – 183

Ms Jie Yen Fan

In this talk, I will introduce local Brownian motions,which are processes that behave like a Brownian mo-tion within a proximity of time, for any time. Con-structions of such processes and some propertieswill be given. Joint work with Eduard Biche, KaisHamza and Fima Klebaner.

19.7. Brownian motion in multiply connectedplanar domainsLaurence Field (Australian National University)

16:25 Wed 4 December 2019 – 183

Dr Laurence Field

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In recent years the relevance of Brownian motion toquestions of conformal mapping has become morevisible. The uniformisation of finitely connecteddomains to certain classes of canonical referencedomains is a classical result of Koebe. One suchclass is the half-plane minus points and horizontalslits, and the corresponding uniformising maps havebeen reinterpreted by Lawler in terms of excursion-reflected Brownian motion, a Markov process thatis Brownian motion while inside the domain with acertain reflection condition at each boundary com-ponent. Drenning also showed that ERBM can alsobe used to analyse Loewner equations in multiplyconnected domains. I will discuss these results andpossible extensions to other classes of reference do-mains.

19.8. Poisson-Dirichlet and Ewens samplingformula approximations for Wright-Fisher modelsHan Gan (Northwestern University)

16:00 Tue 3 December 2019 – 183

Han Gan, Nathan Ross

The Poisson-Dirichlet distribution is a probabilitymeasure on the infinite dimensional ordered sim-plex, and its applications appear in a wide varietyof applications in combinatorics, population genet-ics and Bayesian nonparameterics, to name a few. Itis also intricately related with the celebrated Ewenssampling formula. In this talk we will give errorbounds in the approximation of the frequencies oftypes for the Wright-Fisher model with infinite alle-les mutation structure. This will also lead to a boundon the error between the distribution of the parti-tion generated from sampling from a Wright-Fishermodel and the Ewens sampling formula.

19.9. Forward and Backward in time. PopulationGenetics Stochastic Process ModelsRobert Charles Griffiths (Monash University)

15:10 Tue 3 December 2019 – 183

Prof Robert Charles Griffiths

Classical stochastic process models in populationgenetics describe how a population of genes evolvesforward in time under random drift, mutation,selection and recombination. Examples are theWright-Fisher diffusion process; Moran models,which are birth and death processes; and Lambda-Fleming-Viot models, which are jump processes.Coalescent models, which are random trees orgraphs, describe the ancestral lineages of samplesof genes back in time. These backward and forwardmodels belong together technically as dual stochas-tic processes. This talk will discuss examples ofthese pairs of forward and backward in time models.

19.10. Matching marginals and sumsKais Hamza (Monash University)

14:45 Wed 4 December 2019 – 183

Assoc Prof Kais Hamza

For a given set of random variables X1, . . . , Xd weseek as large a family as possible of random variablesY1, . . . ,Yd such that the marginal laws and the laws

of the sums match: Yid=Xi and

∑i Yi

d= ∑i Xi . Under

the assumption that X1, . . . , Xd are independent andbelong to any of the Meixner classes, we give a fullcharacterisation of the random variables Y1, . . . ,Yd

and propose a practical construction by means of afinite mean square expansion. When X1, . . . , Xd areidentically distributed but not necessarily indepen-dent, using a symmetry-balancing approach we pro-vide a universal construction with sufficient symme-try to satisfy the more stringent requirement that, for

any symmetric function g , g (Y )d=g (X ).

This is joint work with Robert Griffiths.

19.11. The asymptotic behaviour of thetime-varying supermarket modelHermanus Marinus Jansen (The University of

Queensland)

15:10 Fri 6 December 2019 – 183

Mr Hermanus Marinus Jansen

In the supermarket model, there are n parallelservers, each having its own queue. Arriving cus-tomers select d queues at random and join theshortest among them. Much is known about thismodel if its parameters are constant, but it is notclear how it behaves if the arrival rate varies through-out the day, for instance. In this talk, we take a closerlook at the supermarket model with time-varyingparameters under the Join-the-Shortest-Queuepolicy (the special case in which d = n). We explorein particular how the time-varying nature of theparameters influences this model on the diffusionscale as the number of servers becomes large.

19.12. Effect of small noise leading to randominitial conditions in dynamical systemsFima Klebaner (Monash University)

13:55 Fri 6 December 2019 – 183

Prof Fima Klebaner

We study small random perturbations of non-lineardynamics in the vicinity of an unstable fixed point.The classical result on small random perturbationsstates that the effect of noise on a smooth dynami-cal system on any finite time interval [0,T ] vanishesin the limit as the εnoise converges to zero. But thisis not the case when time intervals increase to infin-ity, eg. T = c log(1/ε). The resulting approximationis the corresponding deterministic curve that startsat a random initial condition of the form H(W ). W

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is the large time limit of the scaled linearized sto-chastic dynamics, and H is a limit of the determin-istic non-linear flow H(x) = limt→∞φt (xe−at ). Inthe context of ergodic processes, this gives a com-plimentary result on the cut-off phenomena at crit-icality. This result has applications in biology, suchas PCR and mutations, as well as in physics.

19.13. Interpretation of approximations toinfinitesimal generators asQuasi-Birth-and-Death-like processesAngus Hamilton Lewis (The University of Adelaide)

14:20 Tue 3 December 2019 – 183

Mr Angus Hamilton Lewis

A stochastic fluid process is a two dimensionalMarkov process (J (t ), X (t )), where J (t ) is acontinuous-time Markov chain known as thephase process, and X (t ) is a process with linearincrements driven by J (t ). It is well known thatthe joint probability mass/density of the fluidmodel evolves according to a PDE. By applying theDiscontinuous-Galerkin (DG) method to this PDEwe can approximate the evolution of probabilitydensity over time. Perhaps more interestingly, theDG method also approximates the infinitesimalgenerator of the fluid model, which we can then useto analyse more complex models. The key feature isthat the DG method is able to track both the phaseand the level variables jointly. As a possible meansfor analysing these DG approximations, we showhow the DG approximation to the generator of thefluid model can be viewed as a Quasi-Birth-and-Death-like process.

19.14. Positivity Preserving Numerical Schemesfor Jump-extended CIR/CEV ProcessLibo Li (University of New South Wales)

14:20 Wed 4 December 2019 – 183

Libo Li

We propose a positivity preserving implicit Euler—Maruyama scheme for a jump-extended constantelasticity of variance (CEV) process where the jumpsare governed by a compensated spectrally positivealpha-stable process for alpha in (1,2). Different tothe existing positivity preserving numerical schemesfor jump-extended CIR or CEV process, the modelconsidered here has infinite activity jumps. For thisspecific model, we calculate the strong rate of con-vergence.

19.15. Multivariate Lévy-drivenOrnstein-Uhlenbeck processes Using WeakSubordinationKevin Lu (Australian National University)

16:00 Wed 4 December 2019 – 183

Kevin Lu

Weak subordination is an operation that createstime-changed Lévy processes while allowing thesubordinate to have dependent components. Basedon recent results on self-decomposability of theseprocesses, and focusing specifically on the weakvariance alpha-gamma process, which is a mul-tivariate generalisation of the variance gammaprocess using weak subordination, we constructLévy-driven Ornstein-Uhlenbeck processes withthe weak variance alpha-gamma process as thedriving process or as the marginal distribution.Such processes incorporate autocorrelation andhave applications in the financial modelling ofstationary series. Specifically, we study calibrationfor the stationary solution of these Lévy-drivenOrnstein-Uhlenbeck processes based on discrete-time observations. We derive a likelihood functionusing Fourier inversion, develop a stepwise pro-cedure for estimation, and highlight our resultsin a simulation study. This extends the work ofValdivieso, Schoutens, Tuerlinckx (2009) to themultivariate setting.

19.16. Weak Subordination of Lévy processes onHilbert spacesadam nie (Australian National University)

17:40 Tue 3 December 2019 – 183

Mr Adam Nie

Let (X ,T ) be a pair of Lévy processes on Rd whereT is a multivariate subordinator. It is known thatthe strong subordination of (X ,T ), i.e. the composi-tion X (T (t )) := ∑

n Xn(Tn(t ))en , does not in generalproduce another Lévy process, unless for example Xhas independent components or all Tn ’s are indis-tinguishable. The weak subordination, constructedby Buchmann, Lu and Madan, introduces anotheroperation X ¯ T on (X ,T ) which produces a Lévyprocess that generalises traditional subordination invery intuitive ways.

We extend this construction to an infinite dimen-sional setting where X takes values in an arbitraryseparable Hilbert space H . We define and char-acterise subordinators on the positive cone of aweighted sequence space `1,w with weights de-creasing to zero, and give conditions for the law ofT to concentrate on the sub-cone `+∞. We then givesufficient conditions for a measure defined on theBorel sets of H ⊕ `+∞ to be a Lévy measure, whichis then used to show the weak subordination X ¯Tproduces another Lévy process. The characteristictriplet of the process X ¯T is shown to be a directgeneralization of Buchman et al.

19.17. Stochastic hyperbolic diffusion equationson the sphereAndriy Olenko (La Trobe University)

14:20 Fri 6 December 2019 – 183

Prof Phil Broadbridge, Dr Andriy Olenko

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We introduce stochastic fields generated by partialdifferential equations on the unit sphere. TheCauchy problem for a hyperbolic diffusion equationwith random initial conditions is studied. The exactsolution in terms of a series expansion is given.An approximation to the solution is provided andanalysed by finitely truncating the series expansion.The upper bounds for the convergence rates ofthe approximation errors are derived. Smoothnessproperties of the solution and its approximationare investigated. It is demonstrated that the sampleHolder continuity of this spherical random field isrelated to the decay of the angular power spectrum.Numerical studies of approximations to the solu-tion and applications to real data are presented toillustrate the theoretical results.

The presentation is based on recent joint results withA.D.Kolesnik and N.Leonenko.

19.18. Non-central asymptotics for functionals ofstrong-weak dependent vector random fieldsDareen Omari (La Trobe University)

13:30 Wed 4 December 2019 – 183

Mrs Dareen Omari

In various applications researchers often encountercases involving dependent observations over timeor space. Dependence properties of a random pro-cess are usually characterised by the asymptotic be-haviour of its covariance function. The available lit-erature, except a few publications, addresses limittheorems and reduction principles for functionalsof weakly or strongly dependent random fields sep-arately. For scalar-valued random fields it is suffi-cient as such fields can exhibit only one type of de-pendence. However, for vector random fields thereare various cases with different dependence struc-tures of components. Such scenarios are impor-tant when one aggregates spatial data with differ-ent properties. For example, brain images of differ-ent patients or GIS data from different regions. Weconsider functionals of vector random fields whichhave both strongly and weakly dependent compo-nents. The main results demonstrate that the as-ymptotic behaviour of such functionals is not nec-essarily determined by their Hermite ranks. As anapplication of the new reduction principle we pro-vide some limit theorems for vector random fields.In particular, we show that it is possible to obtaina non-Gaussian behaviour for the first Minkowskifunctional of the Student random field built on dif-ferent memory type components.

19.19. Exponential decay for the exit probabilityfrom slabs of random walk in random environmentAlejandro Francisco Ramirez (Catholic University of

Chile)

16:25 Tue 3 December 2019 – 183

Prof Alejandro Francisco Ramirez

It is believed that in dimensions d ≥ 2 any randomwalk in an i.i.d. uniformly elliptic random environ-ment (RWRE) on Z d which is directionally transientis ballistic. In 2001 and 2002 Sznitman introducedthe ballisticity conditions (T ) and (T ′), as a way toquantify the gap which would be needed to proveaffirmatively this question. The first one is the re-quirement that certain unlikely quenched exit prob-abilities from a set of slabs decay exponentially fastwith their width L. The second one is the require-ment that for all γ ∈ (0,1) the decay is like exp(−C Lγ)for some C > 0. In this talk we present a proof of aconjecture of Sznitman of 2002, stating that (T ) and(T ′) are equivalent. This is a joint work with EnriqueGuerra.

19.20. A model for cell proliferation in adeveloping organismPeter Taylor (The University of Melbourne)

13:30 Fri 6 December 2019 – 183

Phil Pollett, Peter Taylor and Laleh Tafakori

In mathematical biology, there is a great deal of in-terest in producing continuum models by scalingdiscrete agent-based models, governed by local sto-chastic rules. We shall discuss a particular exam-ple of this approach: a model for the way in whichthe neural crest cells that make up the enteric ner-vous system proliferate along a growing gut. Ourstarting point is a discrete-state, continuous-timeMarkov chain model proposed by Hywood, Hackett-Jones and Landman.

We exploit the relationship between the above-mentioned Markov chain model and the well-known Yule-Furry process to derive the exact formof the scaled version of the process. We use this toprovide expressions for features of the occupancyprocess, such as the expected value and varianceof the marginal occupancy at a particular site, thedistribution of the mass of domain agents locatedup to any given point in the domain as well aslimiting results for the above measures.

19.21. Information percolation and the couplingtime of the stochastic Ising modelZongzheng Zhou (Monash University)

16:50 Tue 3 December 2019 – 183

Dr Zongzheng Zhou

In this talk, we will discuss the running time of acoupling-from-the-past algorithm of the stochasticIsing model. There is a parameter β in the Isingmodel which is for controlling the strength of de-pendence. When β = 0 (zero dependence), the run-ning time simply corresponds to a coupon collect-ing time, for which Erdos and Rényi proved that thestandardised running time converges to a Gumbeldistribution. In our work, we proved that a similarlimit theorem holds up to a finite positive β. The

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proof relies on the compound Poisson approxima-tion and an information percolation method.

126

20. Representation Theory

20.1. Classification of blocks in category OKevin Coulembier (The University of Sydney)

13:55 Wed 4 December 2019 – G62

Dr Kevin Coulembier

Work of Jantzen, Soergel and others establishedmany equivalences between blocks in categoryO for semisimple Lie algebras. By developingtechniques related to quasi-hereditary algebrasand Bruhat orders we will turn those results intoa full classification of blocks in category O up toequivalence.

20.2. Classification of relaxed highest-weightmodules for admissible level Bershadsky-PolyakovalgebrasZachary Fehily (The University of Melbourne)

14:45 Wed 4 December 2019 – G62

Zachary Fehily

In this talk, I will present some general featuresof the representation theory of vertex operatoralgebras (VOAs) and the construction of W-algebrasby quantum Hamiltonian reduction. Then I willdescribe some of my recent progress in under-standing the representations of the admissible-levelBershadsky-Polyakov algebras. This constitutes aclass of non-rational W-algebras where represen-tations, characters and modular transformationsare within reach. These results will also assist inunderstanding the representations underlying theadmissible-level WZW models associated with sl3.

20.3. Geometric Langlands for WildHypergeometric SheavesMasoud Kamgarpour (University of Queensland)

15:35 Wed 4 December 2019 – G62

Dr Masoud Kamgarpour

One of the main goals of the geometric Langlandsprogram is to associate to every local system on asmooth curve, a Hecke eigensheaf on the moduliof bundles, equipped with appropriate level struc-tures. When the curve is complete (the so calledunramified case), the existence of the Hecke eigen-sheaf was established by Deligne, Drinfeld, Laumon,and Frenkel–Gaitsgory–Vilonen. However, there hasbeen little progress in the ramified case.

Hypergeometric sheaves are important classes oframified local systems. Their origin traces back tothe seminal work of Riemann on Gauss’s hyperge-ometric function. In modern times, the subject ofhypergeometric sheaves was rejuvenated by Katz.In this talk, I will explain how one can explicitlyconstruct the Hecke eigensheaf associated to wildlyramified hypergeometric sheaves. The key tool weuse is Yun’s notion of rigid automorphic data.

Based on joint work with Lingfei Yi.

20.4. Cohomology of line bundles on flag varietiesLinyuan Liu (The University of Sydney)

16:50 Wed 4 December 2019 – G62

Dr Linyuan Liu

The cohomology of line bundles on flag varieties isa natural and important object in the representa-tion theory of reductive algebraic groups. I will firsttalk about the theory in characteristic zero and someprevious results in positive characteristic. Then I willtalk about the results obtained in my thesis for thethree dimensional flag variety in positive character-istic, which is the first non-trivial case.

20.5. A gallery model for affine flag varietiesYusra Naqvi (The University of Sydney)

17:15 Wed 4 December 2019 – G62

Elizabeth Milicevic, Yusra Naqvi, Petra Schwer and Anne

Thomas

Positively folded galleries arise as images of retrac-tions of minimal galleries in Bruhat-Tits buildingsand they play a role in many areas of maths in-cluding the study of affine Hecke algebras, Macdon-ald polynomials, MV-polytopes, and affine Deligne-Lusztig varieties. In this talk, we will define positivelyfolded galleries and then look at a new recursive de-scription of the set of end alcoves of these galleries,giving us a combinatorial description of certain dou-ble coset intersections in the affine flag variety.

20.6. Representations of affine vertex algebras:beyond category O

David Ridout (The University of Melbourne)

14:20 Wed 4 December 2019 – G62

Dr David Ridout

Affine vertex algebras are among the best-studiedexamples of their kind. However, these studies usu-ally focus on their highest-weight modules. Recentadvances in physics, namely in logarithmic confor-mal field theory and the 4d-2d correspondence withsupersymmetric gauge theories, show that highest-weight modules are not sufficient for these applica-tions. I shall present an approach based on Math-ieu’s twisted localisation functors and coherent fam-ilies that allows one to classify all weight modules(with finite-dimensional weight spaces) for an arbi-trary affine vertex algebra, if the highest-weight clas-sification is already known.

Joint work with Kazuya Kawasetsu.

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20. Representation Theory

20.7. Contravariant forms on Whittaker modulesAnna Romanov (The University of Sydney)

13:30 Wed 4 December 2019 – G62

Dr Anna Romanov

Let g be a complex semisimple Lie algebra. Con-travariant forms are symmetric bilinear forms ong-modules which are invariant under the trans-pose antiautomorphism of the Lie algebra. Manywell-studied classes of g-modules, such as Vermamodules and irreducible finite-dimensional mod-ules, admit a unique contravariant form up toscaling. In the 1970s, Kostant introduced a classof g-modules which naturally generalize Vermamodules called Whittaker modules. These modulesare irreducible and infinite-dimensional. UnlikeVerma modules, Kostant’s Whittaker modules admitmany linearly independent contravariant forms. Inthis talk, I’ll describe joint work with Adam Brownwhich establishes that the dimension of the space ofall contravariant forms on such a module is given bythe cardinality of the Weyl group.

20.8. Crystal structures for canonical GrothendieckfunctionsTravis Scrimshaw (The University of Queensland)

17:40 Wed 4 December 2019 – G62

Dr Travis Scrimshaw

To describe the K-theory ring of the Grassmannian,Grothendeick polynomials are the basis correspond-ing to Schubert varieties. By taking the stable lim-its, symmetric Grothendieck functions Gλ are con-structed, which we can use to form a basis for thering of symmetric functions. By applying theω invo-lution, which sends the Schur function sλ → sλ′ forthe conjugate shapeλ′, we obtain the weak symmet-ric Grothendieck functions Jλ := ωGλ. Yeliussizovconstructed a common generalization that he calledthe canonical Grothedieck functions.

The (resp. weak) (resp. canonical) symmetricGrothendieck functions are known to describedas the sum over set-valued (resp. multiset-valued)(resp. hook-valued) tableaux. Furthermore, set-valued tableaux are known to have a type An crystalstructure by modifying the usual semistandardtableaux crystal structure that comes from Kashi-wara’s theory of crystal bases on highest weightrepresentations. In this talk, we give analogous re-sults for multiset-valued and hook-valued tableaux,which shows that canonical Grothendieck functionsare Schur-positive as an immediate corollary.

20.9. Real Groups, Hodge Theory, and theLanglands dualityKari Vilonen (The University of Melbourne)

16:00 Wed 4 December 2019 – G62

Prof Kari Vilonen

I will explain how Hodge modules enter the repre-sentation theory of real groups. In particular, I willexplain the conjectures of Schmid and myself andwhat is known about them.

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21. Topology

21.1. Deformation of Curves and TopologicalRecursionsWee chaimanowong (AMSI/University of Melbourne)

17:15 Wed 4 December 2019 – 137

Mr Wee chaimanowong

In 2017 Baraglia and Huang studied the SpecialKahler geometry that arises from the moduli spaceof Higgs Bundles. They showed that the genuszero part of the topological recursion invariants ofEynard and Orantin compute the prepotential forthe Special Kahler structure. In this talk we presentan alternative approach to prove this result usingAiry Structures of Kontsevich and Soibelman, andwe propose a possible generalization.

21.2. Local topological recursion governs theenumeration of lattice points in M g ,n

Anupam Chaudhuri (Monash University)

13:55 Wed 4 December 2019 – 137

Mr Anupam Chaudhuri

The moduli space of curves has a cell decompositionin which each cell possesses the natural structureof a convex polytope. Norbury counted the latticepoints in these convex polytopes and showed thatthe enumeration contains in-depth informationabout the moduli space itself. He furthermoreproved that the enumeration is governed by topo-logical recursion. Do and Norbury introduced theanalogous enumeration of lattice points in theDeligne–Mumford compactification of the modulispace of curves. Furthermore, they ask whether theenumeration is governed by the topological recur-sion. In this talk, we will discuss this enumerativeproblem and show that it does indeed satisfy a localversion of the topological recursion.

21.3. On the Goulden–Jackson–Vakil conjecturefor double Hurwitz numbersNorman Do (Monash University)

17:40 Wed 4 December 2019 – 137

Dr Norman Do

Hurwitz numbers enumerate branched covers ofthe sphere with prescribed ramification. Over thelast two decades, they have received a great dealof attention in the literature, due to connectionswith algebraic geometry, representation theory andmathematical physics. The celebrated ELSV formulaexpresses single Hurwitz numbers as intersectionnumbers on moduli spaces of curves, from whichit follows that they exhibit polynomial behaviour.Goulden, Jackson and Vakil showed that one-partdouble Hurwitz numbers are also polynomial,leading them to conjecture that they too arise asintersection numbers on some unidentified moduli

spaces. In recent work with Danilo Lewanski, wegive three partial resolutions to this conjecture,with our formulas leading to non-trivial relationsbetween intersection numbers on moduli spaces ofcurves. In this talk, we will tell some of this story andpresent a precise statement of our results.

21.4. The Mapping Class Group Action on theCharacter Variety of the Once-Punctured TorusGrace Garden (The University of Sydney)

16:00 Wed 4 December 2019 – 137

Ms Grace Garden

We follow the lead of Goldman in the study the ac-tion of the mapping class group on the SL(2, C)-character variety of the once-punctured torus. Theaction of the mapping class group in this contextcan be reduced to the action of polynomial auto-morphisms on the level sets of a specific polynomial,which corresponds to the trace of a peripheral ele-ment. One of the level sets is identified with Teich-müller space and with the hyperbolic plane. We de-scribe two methods based on linear recurrence rela-tions and hyperbolic geometry to extend the actionof the mapping class group SL(2,Z) on the charac-ter variety to an action of the group SL(2,R). The twomethods provide consistent results, which suggeststhe extension of the action to SL(2,R) is natural.

21.5. The topological period-index problemXing Gu (AMSI/University of Melbourne)

15:10 Fri 6 December 2019 – 137

Dr Xing Gu

The topological period-index problem (TPIP), ananalogue to the long-standing period-index prob-lem in algebraic geometry, concerns a given tor-sion class α in the 3rd integral cohomology groupof a topological space X and various principal PUn-bundles over X associated to α. Here PUn is theprojective unitary group of order n, i.e., the unitarygroup Un modulo invertible scalars.

In this talk I will introduce recent work, joint withCrowley, Grant and Haesemeyer on the topologicalperiod-index problems over finite CW-complexesand manifolds.

21.6. Geometric Triangulations and Highly TwistedKnotsSophie Ham (Monash University)

16:50 Tue 3 December 2019 – 137

Ms Sophie Ham

It remains an open question as to whether everycusped hyperbolic 3-manifold admits a geometrictriangulation. Indeed, it is still unknown whether

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21. Topology

every knot complement admits a geometric triangu-lation. We prove that every highly twisted knot ad-mits a geometric triangulation. Highly twisted linksare obtained by Dehn filling a parent link, called afully augmented link. In this talk, we review fullyaugmented links and their geometry, and show thatthey admit geometric triangulations with nice prop-erties. We then describe a certain decomposition ofa solid torus into ideal tetrahedra which will allow usto prove our main result. We end the talk with a dis-cussion of some effective examples.

21.7. Complex Linking Numbers for Strata ofVarietiesMartin Helmer (Australian National University)

13:55 Fri 6 December 2019 – 137

Dr Martin Helmer

Goresky and MacPherson’s stratified Morse theorydefines the complex link of a pair of strata for anyWhitney stratified space; we call the Euler character-istic of the complex link the complex linking num-ber. We consider a Whitney stratification of an al-gebraic variety V . Given two strata X and Y , withX contained in the closure of Y , we show that thecomplex linking number is equal to the Hilbert-Samuel multiplicity of the closure of X inside theclosure of Y . This leads to a new expression forMacPherson’s local Euler obstruction of V in termsof Hilbert-Samuel multiplicities and provides an ef-fective method of the computation of local Euler ob-structions and linking numbers. This is joint workwith Vidit Nanda (Oxford).

21.8. Constructing geometric structures usingtwisted tetrahedraCraig Hodgson (The University of Melbourne)

17:15 Tue 3 December 2019 – 137

Dr Craig Hodgson

The use of ideal triangulations to construct hyper-bolic structures on 3-manifolds is a very powerfultechnique, introduced by Bill Thurston and imple-mented by Jeff Weeks in the computer programsSnapPea and SnapPy. However, this approach failsin some cases, including certain Dehn fillings on thefigure eight knot complement. This talk will describeanother approach to constructing hyperbolic, Eu-clidean and spherical structures using special fun-damental domains built from “twisted tetrahedra”,which are 3-cells with four right-angled hexagons asfaces. This is based on joint work with James Dowtyand Adam Wood.

21.9. Combinatorial isotopiesBoris Lishak (The University of Sydney)

16:00 Tue 3 December 2019 – 137

Dr Boris Lishak

We will show that piecewise linear isotopies of sub-manifolds can be represented by elementary combi-natorial moves. Then we consider an application.

21.10. Homotopy Merge Trees in Topological DataAnalysisKelly Maggs (The Australian National University)

16:25 Tue 3 December 2019 – 137

Kelly Maggs

Persistent homology is the cornerstone of TDA. Anatural question is whether the same ethos of per-sistence can be applied in the homotopy setting. Ex-isting theory has mainly focused on the case where afiltered topological space is path connected. By ex-tending Morozov’s definition of a topological mergetree, we introduce a new algebraic object - the ho-motopy merge tree - to deal with applications wherefiltering the homotopy groups of each filtered pathcomponent is of interest. We prove that our objectsatisfies three key properties:

- Stability: we can define an interleaving distance onour objects that satisfies the stability property. - Uni-versality: we can recover the information about thepersistent homology groups in all filtered path com-ponents at once. - Computability: we describe analgorithm to compute the homotopy merge tree inthe first dimension, i.e. the fundamental group.

21.11. Geometry and physics of circle packingsDaniel Mathews (Monash University)

13:30 Wed 4 December 2019 – 137

Dr Daniel Mathews

I’ll discuss some recent work in progress relatingcircle packings to various ideas in geometry andphysics.

21.12. On the topological recursion for doubleHurwitz numbersEllena Moskovsky (Monash University)

14:45 Wed 4 December 2019 – 137

Ellena Moskovsky

Hurwitz numbers enumerate branched covers of theRiemann sphere with specified branching. SingleHurwitz numbers have been shown to satisfy a poly-nomiality structure, and this was then used to provethat they are governed by the topological recursionof Chekhov, Eynard and Orantin. In this talk, wewill discuss recent work with Borot, Do, Karev, andLewanski, in which we prove analogous results in themore general setting of double Hurwitz numbers. Fi-nally, we will mention some consequences in alge-braic geometry.

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21. Topology

21.13. The Sullivan-conjecture in complexdimension 4Csaba Nagy (The University of Melbourne)

15:35 Wed 4 December 2019 – 137

Mr Csaba Nagy

The Sullivan-conjecture claims that complex pro-jective complete intersections are classified upto diffeomorphism by their total degree, Euler-characteristic and Pontryagin-classes. It followsfrom work of Kreck and Traving that the conjectureholds in complex dimension 4 if the total degree isdivisible by 16. In this talk I will present the proof ofthe remaining cases. It is known that the conjectureholds up to connected sum with the exotic 8-sphere(this is a result of Fang and Klaus), so the essentialpart of our proof is understanding the effect of thisoperation on complete intersections. This is jointwork with Diarmuid Crowley.

21.14. Polynomial relations among kappa classeson the moduli space of curvesPaul Norbury (The University of Melbourne)

16:00 Fri 6 December 2019 – 137

Prof Paul Norbury

We contruct an infinite collection of universal. i.e.independent of (g,n), polynomials in the Miller-Morita-Mumford kappa classes, defined over themoduli space of genus g stable curves with n labeledpoints. We conjecture vanishing of these polynomi-als in a range depending on g and n. This is jointwork with Maxim Kazarian.

21.15. The triangulation complexity of fibred3-manifoldsJessica Purcell (Monash University)

15:10 Tue 3 December 2019 – 137

Prof Jessica Purcell

The triangulation complexity of a 3-manifold M isthe minimal number of tetrahedra required to forma triangulation of M. It is a useful invariant, for ex-ample in computational topology, but surprisinglydifficult to compute. We consider the case that M isa closed orientable hyperbolic 3-manifold that fibersover the circle. We show that the triangulation com-plexity of such a manifold is equal to the translationlength of the monodromy action on the mappingclass group of the fibre, up to a bounded factor de-pending only on the genus of the fibre. This is jointwork with Marc Lackenby.

21.16. A descent-theoretic proof of a theorem ofSerreDavid Roberts (The University of Adelaide)

15:35 Fri 6 December 2019 – 137

Dr David Roberts

In response to a letter of Grothendieck, Serre provedthat for a finite CW complex X (or a space homo-topic to one) Br(X ) = Br′(X ), where Br(X ) is theBrauer group and Br′(X ) is the torsion subgroup ofH 3(X ,Z). The proof uses a Postnikov decompositionof a space with divisible homotopy groups. We willgive a new proof that uses ideas from Gabber’s thesisand descent theory for higher stacks, and moreoverextend this to spaces with a finite cover Ui suchthat Br(Ui ) = Br′(Ui ) for each i .

21.17. Modelling homology operations in stringtopologyMarcy Robertson (The University of Melbourne)

13:30 Fri 6 December 2019 – 137

Dr Marcy Robertson

We describe a new algebraic model that capturesgluing operations in a combinatorial model for themoduli space of genus g curves. This talk coversjoint work with L. Bonnatto, S. Chettih, A. Linton, S.Raynor and N. Wahl.

21.18. Airy structures and topological recursionMichael Swaddle (AMSI/University of Melbourne)

16:25 Wed 4 December 2019 – 137

Michael Swaddle

An Airy structure encodes a Lagrangian subvariety ina topological symplectic vector space W . Kontsevichand Soibelman introduce Airy structures, and showthat they lead to topological recursion; which is analgorithm that can produce cohomology classes onthe moduli space of curves (a cohomological fieldtheory). In this talk, we first give details about thisconnection, and explain how to compute the invari-ants in topological recursion from the Airy structure.

21.19. Tautological classes with twistedcoefficientsMehdi Tavakol (The University of Melbourne)

14:20 Wed 4 December 2019 – 137

Dr Mehdi Tavakol

For a natural number g > 1 the moduli space Mg

classifies smooth projective curves of genus g. In1969 Deligne and Mumford proved that this spaceis irreducible and studied some of its fundamen-tal properties. The geometry of moduli spaces ofcurves have been studied extensively since then bypeople from different perspectives. Many questionsabout the geometry of moduli of curves involve theso called tautological classes. They are the most nat-ural classes on the space and appear in many ques-tions about the geometry and topology of the modulispace. There are many interesting open questionsand conjectures about the structure of the tautolog-ical ring. I will discuss a recent joint work with DanPetersen and Qizheng Yin on tautological classeswith twisted coefficients.

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21. Topology

21.20. T-dualities of orbifoldsGuo Chuan Thiang (The University of Adelaide)

16:50 Wed 4 December 2019 – 137

Dr Guo Chuan Thiang

Topological T-duality manages the remarkable featof exchanging inequivalent principal circle bundles,while conserving their twisted K-theories. Similarly,circle-bundles-with-involution may be exchangedwhile conserving twisted Real K-theories. Althoughthese dualities have topological implications, theyhave intrinsic analytic/representation-theoreticingredients. Building on this understanding, K.Gomi and I discovered a zoo of new dualities for flatorbifolds, which even exchanges the easy and hardparts of spectral sequence computations, providinga great service like the classic Fourier transform.

21.21. Braids and shuffle algebrasTriThang Tran (The University of Melbourne)

14:20 Fri 6 December 2019 – 137

Dr TriThang Tran

We will introduce the quantum shuffle algebra andits connection to the homology of braid groups. Asa fun example, we will compute the homology o theconfiguration space of the plane. If time permits, wewill discuss a result with Jordan Ellenberg and CraigWesterland on Malle’s conjecture for function fields.

132

Index of Speakers

Acatrinei, Ciprian Sorin (16.1), 110Aggarwal, Riya (6.1), 79Aksamit, Anna (8.1), 86Al-shakarchi, Shaymaa Shawkat Kadhim (9.1), 89Albion, Seamus (16.2), 110Alodat, Tareq (19.1), 122Amenta, Alex (12.1), 98an Huef, Astrid (1.1), 62Arman, Andrii (5.1), 73Arroyo, Romina Melisa (10.1), 91Arroyo, Romina Melisa (11.1), 95Atnip, Jason (7.1), 83

Baghal Ghaffari, Hamed (12.2), 98Bakhtawar, Ayreena (17.1), 115Ball, Rowena (13.1), 100Barrera Acevedo, Santiago (2.1), 65Batayneh, Fawwaz (7.2), 83Batten, Lynn (5.2), 73Bean, Nigel (19.2), 122Beaton, Nicholas (16.3), 110Bordignon, Matteo (17.2), 115Borger, James (17.3), 115Botev, Zdravko (19.3), 122Brak, Richard (5.3), 73Brook, David Leonard (9.2), 89Bryan, Paul (10.2), 91Bui, Thi Hoa (18.1), 118Bunjamin, Yudhistira Andersen (13.2), 100Burgess, Andrea (5.4), 73Burton, Benjamin (13.3), 100

Capel, Joshua (15.1), 107Cavenagh, Nicholas (5.5), 73chaimanowong, Wee (21.1), 129Chaudhuri, Anupam (21.2), 129Choudhary, Renu (15.2), 107Cirstea, Florica Corina (10.3), 91Clark, Chad Mathew (14.1), 103Clarke, Bryce (4.1), 71Clarke, Michael (6.2), 79Clutterbuck, Julie (10.4), 91Collevecchio, Andrea (19.4), 122Collins, Julia (13.4), 100Cooper, Matthew Kevin (10.5), 91Coulembier, Kevin (20.1), 127Crawford, William (5.6), 74Cully-Hugill, Michaela (17.4), 115

Das, Sukhen (14.2), 103Dau, Son Hoang (5.7), 74

De Vas Gunasekara, Ajani (5.8), 74Dearricott, Owen (11.2), 95Dipierro, Serena (10.6), 91Dizon, Neil Kristofer (18.2), 118Do, Norman (21.3), 129Donhauzer, Illia (19.5), 122Donovan, Diane (15.3), 107Droniou, Jerome (6.3), 79Duong, Xuan (12.3), 98

East, James (2.2), 65Eberhard, Andrew Craig (18.3), 118

Fan, Jie Yen (19.6), 122Farcaseanu, Maria (10.7), 92Farr, Graham (5.9), 74Fehily, Zachary (20.2), 127Ferov, Michal (2.3), 65Fewster-Young, Nicholas (10.8), 92Field, Laurence (16.4), 110Field, Laurence (19.7), 122Flores, Guillermo Javier (12.4), 98Forrester, Peter (16.5), 110Francis, Andrew (14.3), 103Francis, Forrest James (17.5), 115Fresacher, Matthias (5.10), 75Froyland, Gary (7.3), 83

Gaitsgory, Vladimir (18.4), 118Gan, Han (19.8), 123Gao, Peng (17.6), 115Garbali, Alexandr (16.6), 110Garden, Grace (21.4), 129Garner, Richard (2.4), 65Garner, Richard (4.2), 71Garoni, Timothy (16.7), 110Garrido, Alejandra (2.5), 65Gasiorek, Sean (7.4), 83Gell-Redman, Jesse (10.9), 92Giga, Yoshikazu (1.2), 62Gill, Michael James (5.11), 75Gonzalez-Tokman, Cecilia (7.5), 83Gover, A. Rod (11.3), 95Gowty, Adam (5.12), 75Griffiths, Robert Charles (19.9), 123Gu, Xing (21.5), 129Gunawan, Hendra (9.3), 89Guo, Hailong (6.4), 80Guo, Ivan (8.2), 86Guo, Zihua (10.10), 92Guttmann, Tony (16.8), 111

133

Index of Speakers

Hall, Joanne (5.13), 75Ham, Lucy (14.4), 103Ham, Sophie (21.6), 129Hamza, Kais (19.10), 123Harries, Dylan (3.1), 69Hassell, Andrew (12.5), 98Hathi, Shehzad Shabbirbhai (17.7), 115Hazrat, Roozbeh (9.4), 89Hegland, Markus (6.5), 80Helmer, Martin (21.7), 130Helmer, Martin (6.6), 80Hendrey, Kevin (5.14), 75Her, Hai-Long (9.5), 89hewson, timothy (14.5), 103Hillock, Poh (15.4), 107Hodgson, Craig (21.8), 130Holmes, Mark (16.9), 111Horsley, Daniel (5.15), 76

Ioffe, Alexander (18.5), 119Ipsen, Jesper (16.10), 111

Jackson, Deborah (15.5), 107Jackson, Marcel (2.6), 66James, Simon (15.6), 108Jansen, Hermanus Marinus (19.11), 123Jayaraman, Divahar (7.6), 84Jelbart, Sam (7.7), 84Jones, Benjamin (5.16), 76Joshi, Nalini (1.3), 62Joshi, Nalini (13.5), 101Joshi, Nalini (16.11), 111

Kaarnioja, Vesa (5.17), 76Kamgarpour, Masoud (20.3), 127Kandanaarachchi, Sevvandi Priyanvada (10.11),

92Kandanaarachchi, Sevvandi Priyanvada (3.2), 69Kavkani, Parsa (11.4), 95Kesh, Dipak Kumar (14.6), 104Kieburg, Mario (16.12), 111Kim, Edward (8.3), 86Kitsios, Vassili (3.3), 69Klebaner, Fima (19.12), 123Koussas, James Mathew (2.7), 66Kowalski, Tomasz (2.8), 66Krakowski, Krzysztof (11.5), 95Kress, Jonathan (15.7), 108Krieger, Holly (1.4), 62Kruger, Alexander (18.6), 119krzysik, Oliver (6.7), 80Kumbhari, Adarsh (14.7), 104Kwong, Kwok-Kun (10.12), 92

Le Gia, Quoc Thong (6.8), 80Lee, Ethan Simpson (17.8), 116Levitina, Galina (16.13), 111Lewis, Angus Hamilton (19.13), 124Li, Ji (12.6), 98Li, Libo (19.14), 124Li, Libo (8.4), 86

Limanta, Kevin (5.18), 76Lindstrom, Scott Boivin (18.7), 119Lishak, Boris (21.9), 130Liu, Linyuan (20.4), 127Lonsdale, Heather (13.6), 101Loxton, Ryan (18.8), 119Lu, Kevin (19.15), 124Ly, Fu Ken (12.7), 99Lynch, Sean (17.9), 116Lynch, Stephen (10.13), 93

Ma, Yilin (10.14), 93Mack, Matthew (13.7), 101Maggs, Kelly (21.10), 130Mammoliti, Adam (5.19), 76Manzini, Gianmarco (6.9), 81Markowsky, Greg (5.20), 77Mathews, Daniel (13.8), 101Mathews, Daniel (21.11), 130McDougall, Robert (2.9), 66McGuinness, Mark Joseph (6.10), 81McMillan, Benjamin Blake (11.6), 95Mills, Terence (15.8), 108Moeini, Asghar (18.9), 119Moore, Benjamin (17.10), 116Moravec, Primoz (2.10), 66Morrill, Thomas (17.11), 116Moskovsky, Ellena (21.12), 130

Nagy, Csaba (21.13), 131Nam, Kihun (8.5), 86Nandadulal Bairagi, Nandadulal (14.8), 104Naqvi, Yusra (20.5), 127Narita, Makoto (16.14), 111Nasrawi, Abrahim Steve (16.15), 112Neeman, Amnon (2.11), 67Nguyen Duy, Cuong (18.10), 120Nguyen, Trang Thi Thien (12.8), 99nie, adam (19.16), 124Nikolayevsky, Yuri (11.7), 96Ning, WEI (8.6), 86Norbury, Paul (1.5), 62Norbury, Paul (21.14), 131Nugent, Jeremy (11.8), 96

O’Kane, Terry (3.4), 69Obloj, Jan (8.7), 87Olenko, Andriy (19.17), 124Omari, Dareen (19.18), 125Origlia, Marcos (11.9), 96Origlia, Marcos (2.12), 67Ormerod, John (13.9), 101

Palisse, Jennifer (15.10), 108Palisse, Jennifer (15.9), 108Palmer, Kenneth James (7.8), 84Palmer, Kenneth James (8.8), 87Parker, Brett (16.16), 112Pauwels, Bregje (4.3), 71Payne, Michael (5.21), 77Phillips, Collin Grant (13.10), 102

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Index of Speakers

Pineda-Villavicencio, Guillermo (5.22), 77Pooladvand, Pantea (14.9), 104Pulemotov, Artem (10.15), 93Pulemotov, Artem (11.10), 96Purcell, Jessica (13.11), 102Purcell, Jessica (21.15), 131

Quella, Thomas (16.17), 112Quella, Thomas (2.13), 67QUENJEL, El Houssaine (6.11), 81Quinn, Courtney Rose (7.9), 84

Rahman, Anas Abdur (16.18), 112Rajapaksha, Samithree (3.5), 70Ramagge, Jacqui (13.12), 102Ramirez, Alejandro Francisco (19.19), 125Rao, Asha (13.13), 102Ravotti, Davide (7.10), 85Reid, Colin David (2.14), 67Reid, Margaret (16.19), 112Ridout, David (20.6), 127Rieger, Janosch (18.11), 120Rieger, Janosch (6.12), 81Roberts, David (21.16), 131Roberts, David (4.4), 71Robertson, Marcy (13.14), 102Robertson, Marcy (21.17), 131Rock, Christopher P (10.16), 93Roffelsen, Pieter (16.20), 113Romanov, Anna (20.7), 128Roshchina, Vera (18.12), 120Rovelli, Martina (4.5), 71Rylands, Leanne (1.6), 63

Saha, Subhrajyoti (2.15), 67Sakzad, Amin (5.23), 77Samotij, Wojciech (1.7), 63Saunderson, James (18.13), 120Schillewaert, Jeroen (2.16), 68Schlue, Volker (10.17), 93Schlue, Volker (12.9), 99Schmalz, Gerd (11.11), 96Schmalz, Jelena (15.11), 109Scrimshaw, Travis (20.8), 128Seaton, Katherine Anne (16.21), 113Shearman, Donald (15.12), 109Shi, Wenhui (10.18), 94Shore, Julia (14.10), 105Sikora, Adam (12.10), 99Sikora, Joanna (1.8), 63Simonic, Aleksander (17.12), 116Sivasankaran, Anoop (7.11), 85

Smith, Lachlan (7.12), 85Southwell, Angus (5.24), 77Steinberg, Benjamin (1.9), 63Stevenson, Joshua (14.11), 105Stokes, Tim (2.17), 68Strumila, Michelle (4.6), 72Stumpf, Michael (14.12), 105Sukhorukova, Nadia (18.14), 121Sumner, Jeremy (14.13), 105Sun, Jie (18.15), 121Swaddle, Michael (21.18), 131

Tavakol, Mehdi (21.19), 131Taylor, Peter (19.20), 125Tendas, Giacomo (4.7), 72Terauds, Venta (14.14), 105Thiang, Guo Chuan (21.20), 132Thornton, Lauren (2.18), 68Tran, Dinh (16.22), 113Tran, Thanh (6.13), 81Tran, TriThang (21.21), 132Trinh, Allan (16.23), 113Trudgian, Timothy (1.10), 64Trudgian, Timothy (17.13), 116

Ugon, Julien (18.16), 121Ulcigrai, Corinna (1.11), 64Umar, Abdullahi (2.19), 68

Valdinoci, Enrico (10.19), 94Verma, Geetika (9.6), 89Vilonen, Kari (20.9), 128Vollmer, Andreas (11.12), 97

Wang, Shiyi (8.9), 87Ward, Lesley (12.11), 99Wei, Yong (10.20), 94Wheeler, Valentina-Mira (10.21), 94Wheeler, Valentina-Mira (13.15), 102Wu, Chenyan (17.14), 117Wu, Yuhan (10.22), 94

Xia, Binzhou (5.25), 78

Yang, James (8.10), 87Yau, Kam Hung (17.15), 117

Zhang, Jiyuan (16.24), 113Zhang, Lele (Joyce) (3.6), 70Zhang, Rui (5.26), 78Zhou, Sanming (5.27), 78Zhou, Zhou (8.11), 87Zhou, Zongzheng (16.25), 114Zhou, Zongzheng (19.21), 125

135

Documents

ConferenceTimetableSummary - Staging site · 3:10pm Marty Ross: How I teach, why the Mathologer is evil, and other indiscrete thoughts In this shamelessly narcissistic talk I will