2014

Mathematics IISER Pune

Manidipa Pal Mihir Sheth Milan Kumar Das Neha prabhu Prabhat Kushwaha Pralhad Shinde Pranay Goel Punya Plaban Satpathy Purvi Tiwari Rabeya Basu Rama Mishra Rashmi Kulkarni Rohit Joshi Ronnie Sebastian Roshni Patil Soumen Maity Sourajit Basu Steven Spallone Sudhir Pujahari Supriya Pisolkar Sushil Bhunia Tarun Ayitam Tathagata Mandal Tejas Kalelkar Varun K Vivek Mallick Yasmeen Akhtar

A Raghuram Amit Hogadi Anindya Goswami Anisa Chorwadwala Ankita Sharma Anupam Singh Ashwin T A N Ayan Mahalanobis Ayesha Fatima Baskar Balasubramanyam Chaitanya Ambi Chandrasheel Bhagwat Debangana Mukherjee Debargha Banerjee Debasish Karmakar Debraj Roy Diganta Borah Gaurav Sawant Girish Kulkarni Gunja Sachdeva Hitesh Raundal Jatin Majithia Jayant Deshpande Jeeten Patel Jyotirmoy Ganguly Kaneenika Sinha Makarand Sarnobat

Compiling and Editing Anisa Chorwadwala A Raghuram Shanti Kalipatnapu

Photography Sharvari Vadagama, Anupam Kumar Singh, V S Rao, Anisa Chorwadwala IISER Pune Students & Staff Pratima Videotech, Pune

It has been over two years now since I joined IISER Pune and during this time the face of the Mathematics group has changed considerably. The group comprises now of 18 regular faculty members with two more expected to join soon, 2 INSPIRE faculty members, 1 visiting faculty, and 21 PhD students. Several of our 5th year BS MS students are getting selected in highly competitive places: University of Michigan, ISB Hyderabad, INSEAD France, to mention just a few.

The mathematicians at IISER Pune have organized some excellent workshops during the last year: “Indian Women and Mathematics” and “Chevalley Groups” during the summer of 2013, and “Classical Groups and K-theory,” which included a talk by the world-famous mathematician George Lusztig from MIT, in December 2013.

On March 14th of 2013, we released a documentary titled “The Genius of Srinivasa Ramanujan.” Since then I have hosted a screening of this documentary in many places around the world: Max-Planck-Institut für Mathematik, Bonn, Germany, Universite Paris 13, Villetaneuse, France, at the Joint Mathematical Meeting of AMS and MAA in Baltimore, USA, and my own alma mater IIT Kanpur, India; in each of these screenings I spoke about the role that IISER Pune has played in every aspect of the making of this documentary. All in all, it has been a truly rewarding experience for me.

Let me end this message by what I overheard at a recent conference in TIFR: one mathematician tells another “IISER Pune is coming up very well”, and the other says with unabashed respect in his eyes “No, no, IISER Pune has already come up!”

A Raghuram Professor and Coordinator, Mathematics IISER Pune

Welcome Message

Raghuram with Robert Kanigel, the author of Ramanujan’s Biography “The man who knew infinity”.

Amit Hogadi Associate Professor

amit.hogadi@iiserpune.ac.in Amit Hogadi received PhD from Princeton University in 2007. He was at Tata Institute of Fundamental Research (TIFR), Mumbai before joining IISER Pune in December 2013.

Algebraic Geometry One can describe algebraic geometry as the study of varieties, which are spaces defined by vanishing of polynomial equations. I have been interested in moduli spaces which are special types of varieties which parametrize geometric objects.

In the last couple of decades, people have succeeded in applying ideas from topology, especially homotopy theory, to the study of algebraic varieties. This interplay between homotopy theory and algebraic geometry has been one of my latest fascinations.

Currently, I am working on problems which are sometimes clubbed under the title homotopical algebraic geometry and have applications to K-theory, motivic cohomology and also classical topics like Brauer groups.

Selected Publications Fundamental group of quotient singularities (with Indranil Biswas). To appear in International Mathematics Research Notices. Esnault, H. and Hogadi, A. (2012). On the algebraic fundamental group of smooth varieties in characteristic p>0. Transactions of the

American Mathematical Society 364:2429-2442. Hogadi, A. and Mehta, V. (2011). Birational invariance of the S-fundamental group scheme. Pure and Applied Mathematical Quarterly

7(4):1361-1370. Hogadi, A. and Pisolkar, P. (2011). On the cohomology of Witt vectors of p-adic integers and a conjecture of Hesselholt. Journal of

Number Theory 131(10):1797-1807. Hogadi, A. and Xu, C. (2009). Degenerations of rationally connected varieties. Transactions of the American Mathematical Society

361(7):3931-3394.

Anindya Goswami Assistant Professor

anindya@iiserpune.ac.in Anindya Goswami received his PhD from Indian Institute of Science (IISc), Bangalore, India in 2008. Following this, he held postdoctoral positions at the Universiteit Twente in Enschede, The Netherlands; INRIA in Rennes, France; and Technion in Haifa, Israel before joining IISER Pune in 2011.

Stochastic Control – game theory, math finance, queuing networks, renewal processes I am exploring various topics in Applied Probability. Those include generalization of Black-Sholes-Merton PDE for options in semi-Markov modulated market, Föllmer Schweizer decomposition of an unattainable contingent claim, equilibrium of non-cooperative semi-Markov game under ergodic cost, optimal control under risk sensitive cost, portfolio optimization, large deviation limit, fluid limit in queuing network, PDE techniques in stochastic control and differential games etc. I use Markov models, filtering techniques, stochastic calculus, infinitesimal generator for semigroup of operators, mild solution technique for parabolic equations, viscosity solution method for HJB/HJI equations, stability analysis of numerical schemes for solving PDE or IE., convergence of value iteration schemes, marginalization technique in rare event simulation for hybrid processes, martingale formulation for Markov processes etc. Selected Publications Atar, R., Goswami, A. and Shwartz, A. (2014). On the risk-sensitive cost for a Markovian multiclass queue with priority. Electronic

Communications in Probability 19(11):1-13. Atar, R., Goswami, A. and Shwartz, A. (2013). Risk-sensitive control for the parallel server model. SIAM Journal on Control and

Optimization 51:4363-4386. Basak, G.K., Ghosh, M.K. and Goswami, A. (2011). Risk minimizing option pricing for a class of exotic options in a Markov modulated

market. Stochastic Analysis and Applications 29:259-281. Ghosh, M.K., Goswami, A. and Kumar, S.K. (2010). Portfolio optimization in a Markov modulated market: Chapter in Modern Trends

In Controlled Stochastic Processes: Theory and Applications. Luniver Press, pp. 181-195. Ghosh, M.K., Goswami, A. and Kumar, S.K. (2009). Portfolio optimization in a semi-Markov modulated market. Applied Mathematics

& Optimization 60:275-296. Ghosh, M.K. and Goswami, A. (2009). Risk minimizing option pricing in a semi-Markov modulated market. SIAM Journal on Control

and Optimization 48:1519-1541. Ghosh, M.K. and Goswami, A. (2008). Partially observable semi-Markov games with average payoff. Journal of Mathematical Analysis

and Applications 345:26-39.

Anisa M H Chorwadwala Assistant Professor

anisa@iiserpune.ac.in Anisa Chorwadwala received her PhD from the University of Mumbai in 2007. Following this, she held postdoctoral positions at the Institute of Mathematical Sciences (IMSc), Chennai; The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy; and the Tata Institute of Fundamental Research (TIFR), Mumbai. She has been on the faculty of IISER Pune since April 2011.

Shape Optimization Problems My research work falls mainly in the following two branches of Mathematics: Partial differential equations and Riemannian geometry. I work on shape optimization problems including isoperimetric problems. A typical shape optimization problem is to find a shape which is optimal in the sense that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being minimized depends on the solution of a given partial differential equation defined on the variable domain.

We have solved some shape optimization problems for a class of doubly connected domains over Rank-one symmetric spaces of non-compact type. Among the Rank-one symmetric spaces of compact type, we dealt only with the case of Sn, the unit sphere in ℝn+1 with the induced

metric. In fact, we gave a uniform proof for all the three space forms. Here, the functionals to be optimized were the energy functional and the principal frequency associated with the Dirichlet boundary value problem and the Dirichlet Eigenvalue problem respectively, for both linear as well non-linear operators, namely the Laplacian and the p-Laplacian.

Selected Publications Anisa M. H. C. and Mahadevan, R. A shape optimization problem for the p-Laplacian (Submitted). Anisa, M.H.C., Mahadevan, R. and Toledo, F. (2014). On the Faber-Krahn inequality for the Dirichlet p-Laplacian. ESAIM: Control,

Optimisation and Calculus of Variations (Accepted for Publication). Anisa, M.H.C. and Vemuri, M.K. (2012). Two functionals connected to the Laplacian in a class of doubly connected domains on rank

one symmetric spaces of non-compact type. Geometriae Dedicata DOI: 10.1007/s10711-012-9800-7. Anisa, M.H.C. and Aithal, A.R. Convex polygons and the isoperimetric problem in simply connected space forms Mκ

2. The Mathematical Intelligencer (Accepted for Publication).

Anisa, M.H.C. and Aithal, A.R. (2005). On two functionals connected to the Laplacian in a class of doubly connected domains over space forms. Proceedings of the Indian Academy of Sciences (Math. Sci.) 115:93-102.

Moving Plane Method for a punctured ball on the unit sphere

Anupam Kumar Singh Assistant Professor

anupam@iiserpune.ac.in After doing MSc (Mathematics) from Indian Institute of Technology (IIT) Kanpur, Anupam Singh worked for his doctorate at Harish Chandra Research Institute, Allahabad and Indian Statistical Institute (ISI), Bangalore, India and got PhD from ISI in 2007. He held postdoctoral positions at Tata Institute of Fundamental Research (TIFR), Mumbai and Institute of Mathematical Sciences (IMSc), Chennai, India before joining the faculty of IISER Pune in 2008.

Conjugacy Questions and Representation Theory of Groups Conjugacy questions in group theory have been of interest for its connection with the representation theory and they have not been understood very well for Algebraic Groups over arbitrary field. Usually groups are difficult objects and one studies them via their representations to get better understanding.

Let G (e.g. GLn) be an algebraic group defined over a field k. We denote the k points of G by G(k) (e.g. GLn(k), SLn(k) etc.). An element t of G(k) is said to be real if it is conjugate to its own inverse in G(k). I have been concerned with finding real elements in algebraic groups. Very interestingly often it relates to finding strongly real elements (the elements which are product of two involutions in G(k)).

Apart from studying structure of real elements in Algebraic Groups over k, I also looked at many examples such as linear groups, orthogonal groups, symplectic groups and the groups of type G2 to get better understanding of the problem. Finding real elements helps in the understanding of real characters of the group which in turn give information about those complex representations of the group which are either orthogonal or symplectic. Selected Publications Gates, Z., Singh, A. and Ryan Vinroot, C. Strongly real classes in finite Unitary groups of odd characteristic. To appear in the Journal

of Group Theory. Kulshrestha, A. and Singh, A. (2011). Real elements and Schur indices of a group. The Mathematics Student 80:73-84. Gill, N. and Singh, A. (2011). Real and strongly real classes in PGLn(q) and quasi-simple covers of PSLn(q). Journal of Group Theory

14:461-489. Gill, N. and Singh, A. (2011). Real and strongly real classes in SLn(q). Journal of Group Theory 14:437-459.

Ayan Mahalanobis Assistant Professor

ayanm@iiserpune.ac.in Ayan Mahalanobis obtained his PhD from Florida Atlantic University, Boca Raton, USA in 2005. He was then a Visiting Assistant Professor at the Stevens Institute of Technology, New Jersey, USA for a few years before joining IISER Pune in 2009.

Public Key Cryptography I work at the intersection of pure mathematics (group theory) and public key cryptography. Cryptography, especially public key cryptography, is the backbone of a modern society. It serves us with the required tools for online transactions and trading, i.e., online commerce. My research aims to find new cryptograhic primitives and to build secure protocols from that. We look for groups in which the discrete logarithm problem is secure. My recent work has shown that the group of non-singular circulant matrices over a finite field has some properties that make them attractive over the discrete logarithm problem on a finite field. This new finding has opened a new avenue in research of public key cryptography. Selected Publications Mahalanobis, A. The ElGamal cryptosystem over circulant matrices (Submitted). Mahalanobis, A. and Shah, J. (2014). A new guess-and-determine attack on the A5/1 stream cipher. Computer and Information

Science 7(1):115-124. Mahalanobis, A. (2013). Are matrices useful in public-key cryptography? International Mathematical Forum 8(39):1939-1953. Mahalanobis, A. The MOR cryptosystem and extra-special p-groups. Proceedings of WCC 2012, Castro Urdiales, Spain July 9-13,

2012 & To appear in Journal of Discrete Mathematics and Cryptography. Mahalanobis, A. (2013). The automorphism group of the group of unitriangular matrices over a field. International Journal of Algebra

7(15):723-733. Mahalanobis, A. (2012). A simple generalization of the ElGamal cryptosystem to non-abelian groups II. Communications in Algebra

40:3583-3596. Mahalanobis, A. (2010). The discrete logarithm problem in the group of non-singular circulant matrices. Groups Complexity

Cryptology 2:83-89.

Baskar Balasubramanyam Assistant Professor

baskar@iiserpune.ac.in Baskar Balasubramanyam completed his PhD from Brandeis University, USA in 2007. In 2007-08, he was a postdoctoral fellow at the Center for Advanced Study in Mathematics at the Ben-Gurion University of the Negev in Israel. Following this, he was a Bateman Instructor at California Institute of Technology, USA during 2008-10. He has been with IISER Pune since September 2010.

Modular Forms and Galois Representations My research interests are in Number Theory. A modular form is essentially a function defined on the complex upper half-plane (everything above the real axis) that behaves in a good way under transformations of certain 2x2 matrices with integer entries. The expansion at infinity of such a function gives us a power series whose coefficients have interesting arithmetic properties. An important example of numbers that arise in such a way is the Ramanujan Tau function τ(n). In order to understand these coefficients, it is useful to consider an object attached to it called the L-function (these are generalizations of the Riemann zeta function).

A Galois group is a set of permutations of roots of an irreducible polynomial. For example, complex conjugation permutes the roots of x2+1. It is possible to represent such permutations by matrices. One of the problems in Number Theory is to try and understand the Galois group by studying its representations. One can also attach L-functions to Galois representations and in some cases modular forms and Galois representations are related through their L-functions.

Selected Publications Balasubramanyam, B., Ghate, E. and Vatsal, V. (2013). On local Galois representations over totally real fields. Manuscripta

Mathematica (Accepted for Publication). Balasubramanyam, B. and Longo, M. (2010). ∧-adic modular symbols over totally real fields. Commenterii Mathematici Helvetici

86:841-865.

Chandrasheel Bhagwat INSPIRE Faculty Fellow

cbhagwat@iiserpune.ac.in Chandrasheel Bhagwat obtained Bachelor of Science in Mathematics from Fergusson College, Pune in 2003 followed by Master of Mathematics at Indian Statistical Institute, Bangalore in 2005. He completed PhD in Mathematics from Tata Institute of Fundamental Research (TIFR) Mumbai, India in 2011 and spent a few months as a post-doctoral fellow at IISER Pune. He has received the DST-INSPIRE faculty award and research grant in 2011 and has joined IISER Pune as a faculty member in March 2012.

Number theory, Representation theory and Spectral theory of symmetric spaces The interplay between arithmetic, spectral theory and geometry was studied by mathematicians like Selberg, Maass, and Sunada among many others. From the last few years, I have been working on the study of arithmetic aspects of the spectral theory and geometry of symmetric spaces. My thesis work involved proving various analogues of the classical number theoretic results in the context of symmetric spaces. I am also interested in the study of analytic properties of the Zeta functions associated to a rank one locally symmetric space, which encode a lot of spectral and geometric data. They can be considered as the spectral counterparts of the Dedekind zeta functions associated to number fields. I would like to look at some of the `inverse problems’ on locally symmetric spaces with the aid of the Zeta functions mentioned above.

In a joint work with Prof C S Rajan and Dr Supriya Pisolkar, we have established some results which relate the notions of weak commensurability (introduced by Prasad and Rapinchuk) and representation equivalence of arithmetic lattices in Lie groups. These notions are in turn related to the geometry and spectral theory of the locally symmetric spaces defined by them.

My recent work with Prof Raghuram establishes period relations for the tensor product of motives which together with the celebrated Deligne’s conjecture; predict the results of a similar nature about the special values of Rankin - Selberg L-functions and Dirichlet L-series. In the future, I would like to work on some the problems associated to special values of L-functions.

Selected Publications Bhagwat, C. and Raghuram, A. (2013). Ratios of periods for tensor product motives (To appear in Mathematics Research Letters) Bhagwat, C., Pisolkar, S. and Rajan, C.S. (2013). Commensurability and representation equivalent arithmetic lattices. International

Mathematics Research Notices DOI: 10.1093/imrn/rns282. Bhagwat, C. and Rajan, C.S. (2011). On a multiplicity one property for the length spectra of even dimensional compact hyperbolic

spaces. Journal of Number Theory DOI: 10.1016/j.jnt.2011.05.009. Bhagwat, C. and Rajan, C.S. (2010). On a spectral analogue of the strong multiplicity one theorem. International Mathematics

Research Notices DOI:10.1093/imrn/rnq243.

Debargha Banerjee Assistant Professor

debargha@iiserpune.ac.in Debargha Banerjee received his PhD degree from Tata institute of Fundamental Research, Mumbai. He earned his Master’s degree in Mathematics from Indian Statistical Institute and BSc from St Xavier’s College, Kolkata. He got the Australian Research council Discovery post-doctoral fellowship for 2 years at the Australian National University, Canberra, Australia. He was a visiting scientist at the IMSC, Chennai, India and later a guest scientist at the Max Planck institute of Mathematics, Bonn, Germany before joining IISER Pune in November 2013.

Automorphic Forms and Arithmetic Geometry In arithmetic geometry, we study the integral solutions of equations. We use the rich theory of modular forms (more generally, automorphic forms) to find these solutions.

My research lies in the intersection of algebra, analysis and geometry.

Modular forms are generalizations of the periodic functions. Automorphic forms are the central focus of my research. The theory of modular forms made major contributions in several important discoveries in modern mathematics, including the proof of Fermat's Last theorem.

So far, I worked on three interesting projects related to this exciting area of mathematics.

In my thesis, under the supervision of Prof Eknath Ghate, I completely determined the endomorphism algebras of these motives. I also extended the results to weight one modular forms. I wish to extend my results to totally real fields and more general motives attached to automorphic forms. I am also interested in modular symbols and special values of L-functions. Modular symbols are bridges between automorphic forms and cohomology theories. In other words, a link between analysis and algebra. In my other work, I developed the theory of differential modular forms for Shimura curves over totally real fields. The differential modular forms are invented by Buium and his collaborators.

Selected Publications Banerjee, D. A note on the Eisenstein elements of prime square level. Proceedings of the American Mathematical Society (To appear) Banerjee, D. (2014). Differential modular forms on Shimura curves over totally real fields. Journal of Number Theory 135:353-373. Banerjee, D. and Ghate, E. (2013). Adjoint lifts and modular endomorphism algebras. Israel Journal of Mathematics 195(2):507-543. Banerjee, D. and Ghate, E. (2011). Crossed product algebras attached to weight one forms. Mathematical Research Letters

18(1):139-149. Banerjee, D., Ghate, E. and Kumar, N. (2010). ∧-adic forms and the Iwasawa main conjecture. Iwasawa Theory of totally real Fields

(Proceedings of a Workshop held at IIT Guwahati, published by Ramanujan Mathematical Society) 2010, No. 12. pp.15-47. Banerjee, D. and S. Krishnamoorthy, The Eisenstein elements inside the space of modular symbols (Submitted).

Diganta Borah Assistant Professor

dborah@iiserpune.ac.in Diganta Borah received his PhD from the Indian Institute of Science (IISc), Bangalore, India in 2010 and was a Research Associate there until 2011. He joined IISER Pune in January 2012.

Several Complex Variables Much of my current work focuses on the study of the intrinsic properties of a Kähler metric, the so called Robin metric, on smoothly bounded pseudoconvex domains in ℂn, n>1. This metric was constructed by N Levenberg and H Yamaguchi using the Robin function that arises from the Green function associated to the standard sum-of-squares Laplacian in ℂn.

Selected Publications Borah, D. (2013). Remarks on the metric Induced by the Robin Function II. Michigan Mathematical Journal 62:581-630. Borah, D. and Verma, K. (2011). Remarks on the metric induced by the Robin function. Indiana University Mathematics Journal

60:751-802.

Jayant V Deshpande Visiting Faculty

jdeshpande@iiserpune.ac.in Jayant Deshpande’s specialization is statistics, particularly nonparametric inference, reliability theory and survival analysis. He has extensive teaching and research experience at Panjab University, Chandigarh; University of Pune; Indian Institute of Technology (IIT) Bombay and at many Universities abroad over the last forty five years. He has joined IISER Pune in August 2012.

Mathematical Statistics My current research is on (i) bounds for the reliability and expected life of coherent systems whose components have lifetimes belonging to certain well established aging classes of probability distributions such as the IFRA class and the NBUFRA class, (ii) modeling the probability distributions of parallel and k-out-of-n systems where the distributions are modified due to load sharing at the epoch of every component failure and (iii) nonparametric tests for testing the constancy or the equality and proportionality of fatality rates of emerging epidemics at one or more locations.

Selected Publications Deshpande, J.V., Isha Dewanb and Naik-Nimbalkar, U.V. (2010). A family of distributions to model load sharing systems. Journal of

Statistical Planning and Inference 140:1441-1451. Lam, K.F., Deshpande, J.V., Lau, E.H., Naik-Nimbalkar, U.V., Yip, P.S., Xu, Y. (2009). A test for constant fatality rate of an emerging

epidemic, with applications to the SARS syndrome in Hong Kong and Beijing. Biometrics 64:869-876. Deshpande, J.V. and Naik-Nimbalkar, U.V. (2007). Comparing relative importance of the same component in a series system in two

environments. Journal of Statistical Planning and Inference 137:3410-3415.

Kaneenika Sinha Assistant Professor

kaneenika@iiserpune.ac.in Kaneenika Sinha completed her PhD from Queen's University, Canada in 2006. She has held postdoctoral fellowships at University of Toronto, University of Alberta and Mathematical Sciences Research Institute, Berkeley. She was an assistant professor in IISER Kolkata before joining IISER Pune in December 2012.

Analytic number theory, Harmonic analysis and Arithmetic geometry My primary research work is concerned with extremal functions in Fourier analysis, equidistribution of Fourier coefficients of modular cusp forms, Eichler-Selberg trace formula and arithmetic of modular curves. Modular forms play an extremely important role in number theory and their Fourier coefficients carry fundamental information about points of elliptic curves over finite fields, values of the partition function, class numbers and representations of integers by quadratic forms. They are essential tools in addressing many fundamental problems in Mathematics, like Fermat's Last Theorem. Modular forms are a special case of automorphic representations and lead to the Langlands program, a theme that drives much of the twenty first century research in number theory and representation theory. My research program focuses on the behavior of the Fourier coefficients of normalized Hecke eigenforms and their connections with Jacobian varieties of modular curves.

My research program in number theory heavily draws ideas and techniques from various mathematical areas, like harmonic analysis and arithmetic geometry. The problems pursued by me are posed in the language of algebra and geometry, where as the techniques used in resolving them come from harmonic analysis. Moreover, a comprehensive understanding of these questions necessitates approaching them from a representation-theoretic point of view.

Selected Publications Bucur, A., David, C., Feigon, B., Lalín, M. and Sinha, K. (2011). Distribution of zeta zeroes of Artin-Schreier covers. Mathematical

Research Letters. Lalín, M. and Sinha, K. (2011). Higher Mahler measure for cyclotomic polynomials and Lehmer's question. The Ramanujan Journal

26:257-294. Ram Murty, M. and Sinha, K. (2010). Factoring newparts of Jacobians of certain modular curves. Proceedings of the American

Mathematical Society 138:3481-3494. Ram Murty, M. and Sinha, K. (2009). Effective equidistribution of eigenvalues of Hecke operators. Journal of Number Theory

129:681-714.

Pranay Goel Assistant Professor

pgoel@iiserpune.ac.in Pranay Goel received his PhD in Physics at the University of Pittsburgh, USA. His postdoctoral work was carried out at the Mathematical Biosciences Institute, The Ohio State University, and at the Laboratory of Biological Modeling, NIDDK, National Institutes of Health, USA. He joined the Mathematics and Biology faculty at IISER Pune in 2009.

Dynamical Systems Modeling of Multiscale Phenomena in Biology Dynamical processes in biology naturally span several systems and multiple scales, both in space and in time. We are interested in studying the dynamical behavior of biological processes through mathematical modeling to complement experimental understanding. My research focuses primarily on theoretical neuroscience, cardiac dynamics and diabetes. Each of these areas is rich with issues that arise from a fundamental need to develop theoretical frameworks, and to handle multiscale dynamics within those.

Our understanding of glucose-stimulated insulin secretion from the pancreatic endocrine tissue, the islets of Langerhans, has developed considerably over the last three decades. Much of my recent work has been related to analyzing some newly proposed models of islet voltage oscillations (called “bursting”) that implicate both ionic as well as metabolic activity as being jointly responsible for function. Simultaneously, we are also interested in modeling and analysis of data collected from patients diagnosed with Type 2 diabetes. This is joint work with researchers at the University of Pune and K. E. M. Hospital, Pune.

Although we are a dry lab, since such research is highly interdisciplinary in nature, we collaborate extensively with experimentalists.

Selected Publications Goel, P. and Sherman, A. (2009). The geometry of bursting in the dual oscillator model of pancreatic beta-cells. SIAM Journal on

Applied Dynamical Systems (SIADS) 8:1664-1693. Goel, P., Sherman, A. and Friedman, A. (2009). Multiscale modeling of electrical and intracellular activity in the pancreas: The islet

Tridomain equations. SIAM Multiscale Modeling and Simulation 7:1609-1642. Zhang, M., Fendler, B. Peercy, B., Goel, P., Bertram, R., Sherman, A., Satin, L. (2008). Long lasting synchronization of calcium

oscillations by cholinergic stimulation in isolated pancreatic islets. Biophysical Journal 95:4676-4688. Higgins, E.R., Goel, P., Puglisi, J.L., Bers, D.M., Cannell, M. and Sneyd, J. (2007). Modeling calcium microdomains using

homogenization. Journal of Theoretical Biology 247:623-644. Goel, P., Sneyd, J. and Friedman, A. (2006). Homogenization of the cell cytoplasm: The calcium bidomain equations. SIAM Multiscale

Modeling and Simulation 5:1045-1062.

Rabeya Basu Assistant Professor

rbasu@iiserpune.ac.in Rabeya Basu received her PhD from Tata Institute of Fundamental Research (TIFR), Mumbai, India in 2007. She then undertook postdoctoral work initially at Harish Chandra Research Institute, Allahabad and later as an NBHM Fellow at the Indian Statistical Institute, Kolkata, India. She was in IISER Kolkata as an assistant professor before joining IISER Pune in 2010.

Unitary Whitehead Group From the late 1950's to the early 1970's several attempts were made to generalize classical groups by constructing a theory which does not depend on the invertibility of 2. In 1966-67, Antony Bak resolved this problem by introducing form rings and form parameter. I am working on recent development of Bak's general quadratic (unitary) groups.

Selected Publications Basu, R. (2011). Absence of torsion for NK1(R) over associative rings. Journal of Algebra and its Applications 10:793-799. Basu, R. and Rao, R.A. (2010). Injective stability for K1of regular rings. Journal of Algebra 323:367-377. Bak, A., Basu, R. and Rao, R.A. (2010). Local-global principle for Transvection groups. Proceedings of the American Mathematical

Society 138:1191-1204. Basu, R., Sridharan, R. (2007). An expository article: On Forster's conjecture and related results. Punjab University Research

Journal.

Rama Mishra Associate Professor

r.mishra@iiserpune.ac.in Rama Mishra has obtained her PhD from Indian Institute of Technology (IIT) Bombay, India in 1994. She spent a few years with Harish Chandra Research Institute, Allahabad and Indian Statistical Institute, Delhi as postdoctoral fellow and then served as a faculty at IIT Kharagpur and IIT Delhi for several years. She worked as a JSPS fellow at Osaka City University, Japan for one year and as a visiting faculty at Boise State University, USA before joining IISER Pune.

Low Dimensional Topology For a reasonably long period of time my research focused around the Polynomial representation of long knots. It was motivated by the issue of settling a long lasting conjecture of Abhayankar. We established the equivalence between polynomial isotopic classes of long knots with the ambient isotopic classes of classical knots. Thus the entire knot theory can be done over polynomial knot category. I am trying to compute some numerical knot invariants such as unknotting number through polynomial knot theory. Quantum topology is one of the emerging research areas. Many knot invariants naturally arise through nice matrix algebra representation of interesting quantum groups. They have been related to several models in statistical mechanics. I would like to explore some models that are related to Singular knot theory. I am also interested in classical knot invariants and their application in mathematics and biological sciences. My joint work with Prof Louis Kauffman on A nodal parity invariants of knotted rigid vertex graphs, discusses the application of this invariant on protein folding classification. Selected Publications Mishra, R. (2012). Polynomial unknotting and singularity index. Kyungpook Mathematical Journal (Accepted for Publication). Kauffman, L. and Mishra, R. (2012). Nodal parity invariants for knotted rigid vertex graphs. Journal of Knot Theory and its

Ramifications (Accepted for Publication). http://arxiv.org/pdf/1202.2176v1.pdf Mishra, R. and Bhushan, S. (2012). Knot theory in understanding proteins. Journal of Mathematical Biology 65:1187-1213. Prabhakar, M. and Mishra, R. (2009). Minimal degree sequence for torus knots of type (p,q). Journal of Knot Theory and its

Ramifications 18:485-491. Prabhakar, M. and Mishra, R. (2009). Polynomial representation for long knots. International Journal of Mathematical Analysis 3:325-

337. Mishra, R. (2006). Polynomial representations of strongly invertible knots and strongly negative amphicheiral knots. Osaka Journal of

Mathematics 43:625-639. Prabhakar, M. and Mishra, R. (2006). Minimal degree sequence of 2–bridge knots. Fundamenta Mathematicae 3:190.

A Raghuram Professor and Coordinator raghuram@iiserpune.ac.in

After getting a BTech in Computer Science and Engineering from Indian Institute of Technology (IIT) Kanpur, Raghuram moved to Mathematics and got a PhD in Mathematics in 2001 from the Tata Institute of Fundamental Research (TIFR), Mumbai, India. He had postdoctoral positions at University of Toronto, Canada and TIFR, Mumbai, India and visiting assistant professorships at Purdue University and University of Iowa, USA. He joined Oklahoma State University, USA in 2006 as a tenure-track assistant professor and was promoted to associate professor with tenure in 2011. He has joined IISER Pune in December 2011 as a Professor and the Coordinator of Mathematics. His research has been partially funded by the National Science Foundation, USA, and the Alexander von Humboldt Foundation, Germany.

Number Theory, Representation Theory and Automorphic Forms My group is currently studying the arithmetic properties of special values of automorphic L-functions.

The earliest prototype of a special value of an L-function is the classical formula by Euler which says that the sum ∑ 1/n^2 of reciprocals of squares of all positive integers is π^2/6. More generally, suppose M = {a_n} is a sequence of numbers coming from some interesting data, for example, a_p can be the number of solutions of an equation modulo a prime p, then a guiding principle in modern number theory says that to study the sequence M one should study the L-function L(s, M) = ∑ a_n/n^s. One can glean much information about the sequence M by studying first the analytic properties, and second the arithmetic properties of L(s,M).

The Langlands program, considered by many as a grand unifying principle in modern mathematics, bridges different areas of mathematics, like geometry (elliptic curves), number theory (Galois representations) and representation theory (automorphic forms). The central theme making these bridges possible is the notion of an L-function.

Our work uses the results and techniques of the Langlands program to prove theorems about special values of various L-functions. These values encode within them a lot of arithmetic and geometric information of the objects to which the L-functions are attached. In earlier work stemming from my thesis, we have also studied the representation theory and harmonic analysis of p-adic groups.

Selected Publications Grobner, H., and Raghuram, A. On the arithmetic of Shalika models and the critical values of L-functions for GL(2n). With an

appendix by Wee Teck Gan. American Journal of Mathematics (Accepted for Publication). Gan, Wee Teck and Raghuram, A. (2012). Arithmeticity for periods of automorphic forms. Proceedings of the International

Colloquium in TIFR on Automorphic Representations and L-functions (To appear). Harder, G. and Raghuram, A. (2011). Eisenstein cohomology and ratios of critical values of Rankin-Selberg L-functions. Comptes

Rendus de l'Académie des Sciences-Series I 349:719-724. Raghuram, A. and Tanabe, N. (2011). Notes on the arithmetic of Hilbert modular forms. Journal of Ramanujan Mathematical Society

26:261-319. Raghuram, A. (2010). On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power L-

functions. International Mathematics Research Notices 334-372 doi:10.1093/imrn/rnp127.

Ronnie Sebastian INSPIRE Faculty Fellow

ronnie@iiserpune.ac.in After a Masters’ in Mathematics and Scientific Computing from Indian Institute of Technology (IIT) Kanpur, Ronnie Sebastian did a PhD with V Srinivas and Indranil Biswas at Tata Institute of Fundamental Research (TIFR), Mumbai. He then pursued postdoctoral research at the Institute of Mathematical Sciences, Chennai; Humboldt University, Berlin as an IMU Berlin Einstein Foundation Fellow; and at the Indian Statistical Institute, Bangalore before joining IISER Pune in May 2013.

Algebraic Geometry My research so far has dealt with questions in algebraic geometry. More specifically, with problems related to cycles on abelian varieties and problems related to moduli of vector bundles on curves and surfaces. In cycles I have been interested in a conjecture of Voevodsky which says that smash equivalence is the same as numerical equivalence. This conjecture has some very nice consequences, for instance, it implies that numerical and homological equivalence coincide, which is suggested by the standard conjectures of Grothendieck. My work on moduli of vector bundles has focused on proving Torelli theorems and theorems on rationality of vector bundles. I am currently focusing on expanding my research to number theory.

Selected Publications Sebastian, R. (2013). Smash nilpotent cycles on varieties dominated by products of curves. Compositio Mathematica 149(9):1511-

1518. Biswas, I. and Sebastian, R. (2013). On rationality of moduli spaces of vector bundles on real Hirzebruch surfaces. Proceedings of

the Indian Academy of Sciences Mathematical Sciences 123(2):213-223.

Soumen Maity Associate Professor

soumen@iiserpune.ac.in Soumen Maity received a PhD from the Theoretical Statistics & Mathematics Unit at Indian Statistical Institute, Kolkata, India in 2002. He has postdoctoral experience from Lund University Sweden; Indian Institute of Management (IIM) Kolkata, India; and University of Ottawa, Canada. Prior to joining IISER Pune in 2009, he served as an assistant professor at Indian Institute of Technology (IIT) Guwahati and Indian Institute of Technology (IIT) Kharagpur, India.

Combinatorics − covering arrays, cryptography, and extremal set theory I am mostly interested in combinatorial problems. More specifically, I have been working on covering arrays on hypergraphs, construction of cryptographically important Boolean functions, and extremal set theory. Covering Arrays on Hypergraphs: Covering arrays are combinatorial structures which extend the notion of orthogonal arrays and have applications in the realm of software and circuit testing. A covering array of strength three is an array with the property that any three rows are qualitatively independent. A covering array is optimal if it has the minimum number of columns among covering arrays with the same number of rows. We work on upper and lower bounds on the size of covering arrays on hypergraphs based on hypergraph homomorphism. Cryptography: Boolean functions are used as nonlinear combining functions in LFSR based stream ciphers. A Boolean function is said to be resilient if its output leaks no information about its input values. My research in this area presents some strategies to modify the bent functions, by toggling some of its outputs, in getting a large class of 1-resilient functions with very good nonlinearity and autocorrelation. Extremal Set Theory: Given a finite set X, the general problem in extremal set theory asks how large or small a family of subsets of X can be if it satisfies certain restrictions. Two core concepts in extremal set theory are intersecting families and shadows. The main results for intersecting families are the Erdos-Ko-Rado and Hilton-Milner theorems, and the principal result for shadows is the Kruskal-Katona theorem. By defining suitable notions of “intersecting” and “shadow” we intend to find remarkable analogs of these theorems for other structures such as multisets, permutations, set partitions, etc. Selected Publications Maity, S., Arackaparambil, C. and Meyase, K. (2013). A new construction of resilient Boolean functions with high nonlinearity. Ars

Combinatoria 109:171-192. Maity, S. (2012). 3-Way software testing with budget constraints. IEICE Trans. Information & Systems E95-D (9):2227-2231. Yasmeen and Maity, S. (2012). Mixed covering arrays on hypergraphs. Communications in Computer and Information Science

305:327-338. Maity, S. and Maitra, S. (2010). Minimum distance between bent and 1-resilient Boolean functions. Ars Combinatoria 97:351-375.

Steven Spallone Associate Professor

sspallone@iiserpune.ac.in Steven Spallone received his PhD from the University of Chicago, USA in 2004. Afterwards he did postdoctoral work at the Max-Planck Institute in Bonn, at Purdue University, and at the University of Oklahoma, USA. He also visited the Tata Institute of Fundamental Research (TIFR) Mumbai, India. He joined the faculty of IISER Pune in July 2012.

Representation Theory and Canonical Forms A basic theme in representation theory for a topological group is the duality between the geometry of the group and its spectral theory. In one project, I study arithmetically interesting representations called “discrete series” using this duality. I attempt to write their multiplicities in terms of measures over conjugacy classes of p-adic groups.

In another project, I study representations of isometry groups of quadratic forms, notably those induced from a stabilizer P of a nondegenerate subspace. I show that relationships between such representations are illuminated by first decomposing P into two subgroups M and N, and then by finding canonical forms for the conjugation action of M on N.

To introduce another project, consider square matrices, with entries modulo a cubefree integer. I study the question of when two such matrices are conjugate. I have also written some papers regarding when two germs of dynamical systems fixing a point are conjugate, in the p-adic setting.

Selected Publications Spallone, S. (2012). Stable trace formulas and discrete series representations. Pacific Math Journal 256:435-488. Jenkins, A. and Spallone, S. (2012). Local analytic conjugacy of semi-hyperbolic mappings in two variables, in the non-archimedean

setting. International Journal of Mathematics 23:1250059. Shahidi, F. and Spallone, S. (2010). Residues of intertwining operators for SO(6) as character identities. Compositio Mathematica

146:772-794. Spallone, S. (2008). Residues of intertwining operators for classical groups. International Mathematics Research Notices 056:37. Margalit, D. and Spallone, S. (2007). A homological recipe for pseudo-Anosovs. Mathematical Research Letters 14:853-863.

Supriya Pisolkar Assistant Professor

supriya@iiserpune.ac.in Supriya Pisolkar obtained her PhD degree from Harish Chandra Research Institute, Allahabad, India in 2010. She was a postdoctoral fellow at Tata Institute of Fundamental Research, Mumbai for about three years before joining IISER Pune in December 2013.

Number Theory, Galois Cohomology, Arithmetic aspects of Symmetric Spaces Broadly speaking, my area of research is number theory and I have been working on problems mostly related to local fields. My thesis deals with questions having a common theme of understanding behavior of norm maps in Galois extensions of local fields. As an application, I computed the Chow group of Zero-cycles of degree zero on Châtelet surfaces over local fields. This work relies on the work of Bloch, Swinnerton-Dyer, Colliot-Téllène, Sansuc.

In joint work with Dr A Hogadi, we proved a conjecture of Hesselholt which predicts the vanishing of the cohomology group H1(G(L/K),W(OL)) for a Galois extension of local fields L/K. This can be seen as an analogue of Hilbert theorem-90. In the future, I would like to work on generalizations of this result.

Over the last couple of years I have also been fascinated by arithmetic aspects of locally symmetric spaces which are special type of manifolds. The theory of locally symmetric spaces is a beautiful amalgamation of theory of Lie groups, algebraic groups, analysis, differential geometry, representation theory. In a joint work with Prof C S Rajan and Dr C Bhagwat we have studied questions related to commensurability type problems of these spaces.

Currently, I am interested in understanding the work of Gopal Prasad and Rapinchuk which establishes a connection between arithmetic and geometric aspects of these spaces, giving rise to series of questions in this area.

Selected Publications Bhagwat, C., Pisolkar, S. and Rajan, C.S. (2013). Commensurability and representation equivalent arithmetic lattices. International

Mathematical Research Notices doi: 10.1093/imrn/rns282. Hogadi, A. and Pisolkar, S. (2013). An equicharacteristic analogue of Hesselholt’s conjecture on cohomology of Witt vectors. Acta

Arithmetica 158(2):165-171. Hogadi, A. and Pisolkar, S. (2011). On the cohomology of Witt vectors of p-adic integers and a conjecture of Hesselholt. Journal of

Number Theory 131(10):1797-1807. Pisolkar, S. (2008). The Chow group of zero-cycles on certain Châtelet surfaces over local fields. Indagationes Mathematicae

19(3):427-439.

Tejas Kalelkar Assistant Professor

tejas@iiserpune.ac.in After completing his MSc from Indian Institute of Technology, Bombay, Tejas Kalelkar got his PhD from Indian Statistical Institute, Bangalore in 2010. He was then a postdoctoral fellow at Institute of Mathematical Sciences, Chennai and a Chauvenet Postdoctoral Fellow at the Washington University in St Louis, USA. He joined IISER Pune in December 2013.

Low Dimensional Topology My area of research is low-dimensional topology. This is a very active area of research with several longstanding conjectures proved fairly recently, like Thurston’s Geometrization conjecture (which implies the Poincare conjecture) and the Virtual Fibering conjecture. Within low-dimensional topology I focus mainly on foliations, triangulations and Heegaard splittings of 3-dimensional manifolds.

A closed book looks like a solid 3-dimensional object, but on closer analysis is observed to consist of 2-dimensional pages stacked tightly together. Similarly, every 3-manifold can be built by stacking 2-dimensional surfaces tightly together into what is called a foliation. I am studying a special class of foliations called taut foliations which tell us useful topological properties of the 3-manifold.

On cutting open a 3-manifold along a special embedded surface, called the Heegaard-splitting surface, we end up with two simple pieces called handlebodies. Every closed 3-manifold has such a splitting surface which may not be unique. I am currently working on a structure for these splitting surfaces when a 3-manifold has infinitely many of them.

Every 3-manifold can be built by suitably sticking tetraheda together. Normal surfaces are surfaces embedded particularly `nicely' with respect to such a triangulation. I have proved several results using normal surfaces, such as a weak converse of Haken’s well-known result about normality of incompressible surfaces with respect to every triangulation of the 3-manifold.

Selected Publications Kalelkar, T. and Roberts, R. Taut foliations in surface bundles with multiple punctures. arXiv:1211.3637, Pacific Journal of

Mathematics (Accepted for Publication). Gadgil, S. and Kalelkar, T. (2013). A Chain complex and Quadrilaterals for normal surfaces. Rocky Mountain Journal of Mathematics,

43(2):479-487. Kalelkar, T. (2009). Incompressibility and normal minimal surfaces. Geometriae Dedicata 142(1):61-70. Kalelkar, T. (2008). Euler characteristic and quadrilaterals of normal surfaces. Proceedings of the Indian Academy of Sciences

Mathematical Sciences 118(2):227-233.

Vivek Mohan Mallick Assistant Professor

vmallick@iiserpune.ac.in After completing BStat (1999) and MStat (2001) from Indian Statistical Institute, Vivek Mallick got his PhD from Tata Institute of Fundamental Research (TIFR) Mumbai, India in 2008. He has joined IISER Pune in 2012 after completing his postdoctoral research at the Institute of Mathematical Sciences in Chennai and Centre de Recerca Matematica in Barcelona, Spain.

Algebraic Geometry My research can be divided into three categories: intersection theory, derived categories, and T-varieties.

Intersection theory In intersection theory, one defines invariants of algebraically defined geometric spaces in terms of how the spaces lying on the given space intersect each other. One can study those invariants to determine deep geometric properties of the space.

Derived category Given a variety (a type of algebraically define geometric space), one can define another algebraic object called derived category. It is known that a lot of the geometric properties of the space translate to algebraic properties of the derived category.

T-variety While studying an object one many times first determine its group of symmetries. The same holds for varieties. When the group of symmetries contain a torus, one can, with some additional hypothesis describe a variety purely in terms of some combinatorial data. Currently I am working on such varieties.

Selected Publications Dubey, U.V. and Mallick, V.M. (2012). Reconstruction of a superscheme from its derived category. Journal of the Ramanujan

Mathematical Society 27(4). Dubey, U.V., Mallick, V.M. (2012). Spectrum of some triangulated categories. Journal of Algebra 364:90-118. Mallick, V.M. (2009). Roitman's theorem for singular projective varieties in arbitrary characteristic. Journal of K-Theory 3:501-531.

S A Katre Professor & Head Department of Mathematics University of Pune, Pune E-mail: sakatre@math.unipune.ac.in sakatre@gmail.com S A Katre received Masters degree in Mathematics from University of Pune and PhD from Panjab University, Chandigarh, India. He began his academic career from SP College of Pune and moved to University of Pune in 1988 as a faculty member and has been there since. Prof Katre’s work is in the area of Algebra and Number Theory, in particular, cyclotomy, number of points on curves over finite fields, Waring's problem for matrices, coding theory, and group theory. His pedagogical interests include contributing to mathematics olympiads, open source mathematical software, and e-learning in mathematics. Prof Katre had served as the editor of pedagological journal Bona Mathematica and has organized the NBHM sponsored ATM Schools in Mathematics during 2004-2012.

Sujatha Ramdorai

Canada Research Chair, Department of Mathematics University of British Columbia, Canada

Sujatha Ramdorai obtained her PhD in TIFR/Bombay University in 1992 and was with TIFR till January 2012. She currently holds a Canada Research Chair at the Department of Mathematics, University of British Columbia. Her research interests include Iwasawa theory and the theory of motives. Prof Ramdorai is a recipient of the Shanti Swarup Bhatnagar Award and the ICTP Ramanujan Award. She was a Member of the National Knowledge Commission and is a Member of the Scientific Advisory Council to the Prime Minister, and also the National Innovation Council. She is also interested in broader educational issues and in policy matters related to Higher Education and Research.

Adjunct Faculty Members

Amlan Barua Postdoctoral Fellow Amlan’s research work focuses primarily on the numerical solution of partial differential equations that are encountered in different fields of applications. Earlier, he had worked on problems of Materials Science where his task was to find effective solvers for boundary integral equations. More lately, he has developed an interest in the field Bio-Mathematics. With Dr Pranay Goel at IISER Pune, he is working on several research projects ranging from clinical biology to numerical simulation of partial differential equations that emerge from the modeling of Islets of Langerhans. Apart from applied mathematics, he is also interested in functional analysis and theoretical partial differential equations. Barua, A., Li, S., Feng, H. and Li, X. (2013). An efficient rescaling algorithm for simulating the evolution of multiple elastic precipitates. Communications in Computational Physics, 14(4):940-959. Feng, H., Barua, A., Li, S. and Li, X. (2013). A parallel adaptive treecode algorithm for evolution of elastically stressed solids, Communications in Computational Physics, 15(2):365-387.

Ayesha Fatima Graduate Student

Ayesha completed BS MS from IISER Pune in 2012. She joined the Mathematics PhD program at the institute in August 2013 and is currently doing coursework as a part of this program.

Debangana Mukherjee Graduate Student Debangana completed MSc in Mathematics from Mount Carmel College, Bangalore in the year 2013 and joined IISER Pune soon after. She is currently doing coursework toward the PhD program in Mathematics at IISER Pune.

Debasish Karmakar

Graduate Student Debasish has joined IISER Pune as a graduate student in Mathematics after completing MSc from Banaras Hindu University, Varanasi. He is interested in Geometry and Number Theory.

Debraj Roy Graduate Student Debraj completed MSc (Mathematics) in 2011 from University of Hyderabad, Hyderabad. He joined IISER Pune in August 2012 and is presently doing coursework that is a part of the IISER Pune Mathematics PhD program.

Research Fellows & Students

Gunja Sachdeva Graduate Student

Gunja completed MPhil in Mathematics from Dayalbagh Educational Institute, Deemed University, Agra in December 2011 and joined IISER Pune in August 2012. She recently finished her minor thesis on Explicit Deterministic Constructions for Membership in the Bitprobe Model, supervised by Dr Soumen Maity. She is currently working towards a PhD under the guidance of Prof A Raghuram in the area of Number Theory.

Gaurav Prabhakar Sawant Graduate Student Gaurav has joined the PhD Program in Mathematics at IISER Pune as a CSIR Junior Research Fellow after completing BS MS Dual degree at the same institute, and is presently doing a one-year coursework as part of this program. He was a Teaching Assistant for the BS MS Course of Linear Algebra, taught by Prof Raghuram, in Fall 2013. Gaurav is interested in geometric notions of algebraic topology, complex analysis, numerical methods and discretization, and their connections to partial differential operators.

Girish Kulkarni Graduate Student

Girish completed MSc Mathematics from IIT Madras in 2010 and MSc from University of Western Ontario, Canada in 2012. Last year he was reading Reflection groups with Prof Shripad Garge at IIT Bombay. He has also taught at Post Graduate Centre for Mathematics at Sir Parashurambhau College, Pune for 3 semesters. Girish joined IISER Pune in 2013 and is presently doing coursework as a part of the Mathematics PhD program.

Hitesh Raundal Graduate Student Hitesh obtained MSc in Applied Mathematics from the University of Hyderabad and joined IISER Pune in January 2011. He is a graduate student with Dr Rama Mishra in the area of knot theory. He has been working on the minimal polynomial representations of knots and their super bridge indices, and trying to build relation between various numerical knot invariants particularly polynomial degree, edge number and super bridge index of knots. His work is mostly concerned with the minimal polynomial representations of knots, polynomial degree of knots and topological properties various spaces of polynomial knots.

Jatin Majithia Graduate Student

Jatin completed his MSc in Mathematics from University of Pune in 2012 and soon after that he joined IISER Pune. He has done with his minor thesis on Pricing option theory under the supervision of Dr Anindya Goswami. His area of interest is algebraic geometry.

Students

Jyotirmoy Ganguly Graduate Student Jyotirmoy completed MSc in Mathematics from University of Hyderabad in 2013 and joined IISER Pune soon after. Presently, he is doing coursework as a part of the Mathematics PhD program at IISER Pune.

Makarand Sarnobat

Graduate Student

Makarand completed MSc in Mathematics from Sir Parshurambhau College in 2012 and joined IISER Pune in August 2012. He is close to completing his minor thesis on Grushko's Theorem under the guidance of Dr. Tejas Kalelkar and is currently reading Algebraic Number theory with Prof A Raghuram.

Manidipa Pal Graduate Student Manidipa has completed MSc from IIT Bombay in 2011. She has joined IISER Pune in January, 2012 and has now completed a one-year coursework as part of the PhD program at IISER Pune. Her research interest is in Algebraic Number Theory.

Milan Kumar Das

Graduate Student Milan completed MSc from Vidyasagar University, West Bengal in 2012. He joined IISER Pune in August 2013 and is presently doing coursework as part of the Mathematics PhD program at the institute.

Neha Prabhu Graduate Student

Neha completed M.Sc. Mathematics from IIT Bombay in 2012 and joined IISER-Pune in August 2012. She recently submitted her minor thesis on Ramanujan Graphs, supervised by Dr. Chandrasheel Bhagwat. She is currently working towards a PhD under the guidance of Dr. Steven Spallone. Her research interests lie in the area of Representation Theory.

Prabhat Kushwaha

Graduate Student

Prabhat completed MSc from the Department of Mathematics, Banares Hindu University, Varanasi and joined IISER Pune in January 2012. He has now completed coursework along with clearing comprehensive exams and is presently working on a minithesis. He is interested in working in the area of Elliptic Curve Cryptography.

Students

Pralhad Shinde Graduate Student

Pralhad completed Masters degree in Mathematics from University of Pune, Pune in 2011. He joined IISER Pune as a graduate student in January 2012 and has undertaken coursework that is part of the IISER Pune Mathematics PhD program. Presently he is doing a minor thesis with Dr Anisa Chorwadwala in shape optimization problems and working with Dr Soumen Maity in the area of combinatorial design theory for the major thesis.

Rashmi Kulkarni Graduate Student

Rashmi obtained MSc in Microbiology from MS University, Baroda and an MTech from the Centre for Modeling and Simulation, University of Pune, Pune. She joined IISER Pune in August 2010 and is working with Dr Pranay Goel toward her PhD. Her research involves quantitating oxidative stress in the development of insulin resistance.

Rohit Joshi

Graduate Student

Rohit has a Masters degree from IIT Kanpur. He has completed coursework and cleared comprehensive exams toward IISER Pune’s PhD program in Mathematics and is currently working with Prof A Raghuram on Representation theory. He was the winner of silver medal in International Mathematics Olympiad in 2004 while in his 12th standard and was chosen as the IISER Pune Mathematics Student of the Year in 2013.

Sudhir Pujahari Graduate Student Sudhir obtained MSc in Mathematics from Utkal University, Orissa. He joined IISER Kolkata in January 2011 as a CSIR JRF and shifted to IISER Pune in December 2012. He is working with Dr Kaneenika Sinha in the area of Analytic Number Theory. Some of his work has recently been submitted (Sign changes of coefficients of certain Dirichlet series (with Meher, J. and Shankhadhar, K.D.).

Sushil Bhunia

Graduate Student

Sushil completed MSc (Mathematics) in 2010 from Jadavpur University, Kolkata, India. He joined IISER Pune in January 2012 and completed coursework along with comprehensive examinations that are part of the graduate program. Now he is working with Dr Anupam Singh in Algebraic groups.

Tathagata Mandal Graduate Student

Tathagata completed his MSc in Mathematics from Visva-Bharati University, Santiniketan, India in 2012. He joined IISER Pune in August 2013 as a graduate student. He is presently doing coursework as a part of the Mathematics PhD program at IISER Pune and is interested in Number Theory and Algebraic Geometry.

Students

Yasmeen Akhtar Graduate Student

Yasmeen completed MSc in Mathematics from University of Pune and joined IISER Pune in January 2011. She is working toward her PhD with Dr Soumen Maity in the area of combinatorics and graph theory. More specifically, her research project is based on strength three covering arrays and hypergraphs.

Ankita Sharma BS MS Student Ankita is working with Dr Pranay Goel at IISER Pune as part of her BS MS fifth year project. Her project is about Game theoretic analysis to show parasitic cooperation at traffic intersections that encompasses conflict.

Punya Plaban Satpathy

BS MS Student

I am currently working on my 5th year project with Prof A Raghuram at IISER Pune on p-adic L-functions for modular forms. The goal of the project is to write down p-adic L-function for Ramanujan delta function in an explicit manner. To do this one has to understand the p-adic L-functions attached to holomorphic cusp forms φ ∈ Sk (Γ0 (N )), i.e., weight k level N forms. The main part of the project is to study Manin’s 1976 paper, which works over a totally real field F and my project is to rewrite his paper specializing F = Q.

Roshni Patil BS MS Student Roshni is doing her fifth year BS MS project at TIFR-CAM, Bangalore and she is working with Prof Prashant K Srinivasan. Her work is focused on the ideas in "Calculus of Variations" related to finding the point of extrema or in general critical points of infinite (as well as finite) dimensional functional.

Tarun Ayitam

BS MS Student

Tarun worked with Prof R Ramanujam in Game Theory. He had done his theory projects in game theory, hypergraphs and computational complexity. Besides Mathematics, he is interested in miscellaneous related areas. He blogs on diverse topics in economics, film-production, marketing and the Indian philosophy. Tarun believes that Mathematics Education helps one in understanding importance of rigor and the central philosophy extends itself into several other spheres. He is an entrepreneur and does science communication through his startup Sciensation. The startup was motivated by the observation that science is usually taught like a religion. He exercises his freedom of speech and debates actively in diverse topics.

Students

Varun K BS MS Student

My primary research interests are in stochastic processes, dynamical systems, mathematical modeling and applied statistics. I am currently working on a mathematical model of 1-carbon and glutathione metabolism with Dr Pranay Goel.

Mihir Sheth BS MS Student Mihir is currently working on his Master's thesis with Baskar Balasubramanyam on the topic of cyclotomic fields and p-adic L-functions. The primary objective of this project is to understand the proof of Iwasawa's Main Conjecture which relates certain Galois actions to p-adic L-functions, and to think about a different way of constructing these functions. Mihir is mainly interested in algebraic number theory and would like to pursue a PhD after graduating from IISER Pune.

Ashwin T A N

BS MS Student

Ashwin is currently doing his fifth year project with Dr Venkateswaran Krishnan at the TIFR Centre for Applicable Mathematics, Bangalore. His work involves applying techniques from microlocal analysis to certain imaging problems. Specifically, he is trying to understand the distribution kernels of certain operators that arise in imaging problems by studying the geometry of their associated canonical relations. Ashwin is interested in the general area of analysis and partial differential equations and plans to pursue a PhD in this field.

Purvi Tiwari BS MS Student Purvi is currently doing her fifth year BS MS project at TIFR-ICTS, Bangalore and working with Prof Amit Apte. She is working on "Parameter estimation of a population dynamics model using Monte Carlo Markov Chain method".

Sourajit Basu

BS MS Student

Sourajit is currently doing his fifth year BS MS project with Soumen Maity in IISER Pune. His thesis concerns looking at analogs of results from extremal set theory such as the Erdos-Ko-Rado, Kruskal Katona and Hilton Milner Theorems to other discrete structures such as vector spaces and multisets.

Students

Jeeten Patel Teaching Assistant

Jeeten graduated with a BS MS Dual degree from IISER Pune in May 2013 and is currently working as a Teaching Assistant. He had assisted Dr Ayan Mahalanobis in conducting Introduction to proofs course, Dr Pranay Goel for Single variable calculus course and Dr Diganta Borah for Analysis for fall semester 2013 & Dr Anindya Goswami in conducting Multivariable calculus for spring semester 2013. He is currently assisting Dr Vivek Mallick in conducting Introduction to computing course and Dr Jayant Deshpande in conducting the Probability and Statistics course. In December 2013, he assisted as copy editor for international proceedings of a week-long workshop entitled “The Bloch Kato conjectures for the Riemann zeta function at the odd positive integers” which was held at IISER Pune, India, in July 2012 which is soon going to be published by Cambridge University Press. Jeeten is interested in Mathematical Finance. He has worked with Dr Anindya Goswami for his MS thesis which is tilted as Pricing and hedging in a GBM market with Markov switching: A survey which involves surveying recent development on certain problems in Mathematical Finance. It aims to survey existing literature on Markov modulated GBM model and make competitive study along with some more models (semi-markov modulated GBM, Levy process). Issues related to locally risk minimizing pricing, optimal hedging, portfolio optimization with risk sensitive cost, stability of numerical solutions of associated PDE’s, computation of complexity of numerical schemes are being emphasized. In addition to this he has research publication with Dr Anindya Goswami for "External cash flow of the optimal hedging in a semi Markov modulated market.

Chaitanya Ambi Teaching Assistant

Suvarna Gharat Administrative Assistant

Suvarna completed her BSc in Physics from Fergusson College and her post graduation from Modern College, Pune. She joined IISER Pune in July 2011 and is presently assisting the Mathematics group in various administrative responsibilities.

Academic and Administrative Support

• Balasubramanyam, B., Ghate, E., Vatsal, V. (2013). On local Galois representations associated to ordinary Hilbert

modular forms. Manuscripta Mathematica, 142:513-524. • Banerjee, D. (2014). Differential modular forms on the Shimura curves over totally real fields. Journal of Number

Theory, 135:353-373. • Basu, R. (2013). An exposition: On the elementary subgroup of GL_n over rings. Mathematics Newsletter, Vol. 24

(2013). • Bhagwat, C.R., Pisolkar, S. and Rajan, C.S. (2013). Commensurability and representation equivalent arithmetic

lattices. International Mathematics Research Notices. (IMRN) doi:10.1093/imrn/rns282. • Bhagwat, C.R. and Raghuram, A. (2013). Ratios of periods for tensor product motives. Mathematical Research

Letters (Accepted for Publication). • Borah, D. (2013). Remarks on the metric induced by the Robin function II. Michigan Mathematics Journal, 62:581-

630. • Chorwadwala, Anisa M.H. and Aithal, A.R. Convex polygons and the isoperimetric problem in simply connected space

forms $M_\kappa^2$''. The Mathematical Intelligencer (Accepted for Publication). • Anisa, M.H.C., Mahadevan, R. and Toledo, F. (2014). On the Faber-Krahn inequality for the Dirichlet p-Laplacian.

ESAIM: Control, Optimisation and Calculus of Variations (Accepted for Publication). • Deshpande, J.V., Lam, K.F., Naik-Nimbalkar, U.V., Xu, Y. Tests for comparing the progression of an epidemic in two

groups. Journal of Indian Statistical Association (Accepted for Publication). • Dwivedi, A. (Sponsor: Goel, P.) A Stochastic Version of the Pedersen-Sherman Insulin Secretion Model. SIAM

Undergraduate Research Online (SIURO) Published electronically Vol. 7. (2014). http://dx.doi.org/10.1137/12S011994.

• Atar, R., Shwartz, A. and Goswami, A. (2013). Risk-sensitive control for the parallel server model. SIAM Journal of Control Optimization, 51:4363-4386.

• Biswas, I. and Hogadi, A. On the fundamental group of a variety with quotient singularities. International Mathematics Research Notices (Accepted for Publication).

• Kalelkar, T. and Roberts, R. Taut foliations in surface bundles with multiple boundary components. Pacific Journal of Mathematics (Accepted for Publication).

• Gadgil, S., and Kalelkar, T. (2013). A chain complex and quadrilaterals for normal surfaces. Rocky Mountain Journal of Mathematics, 43:479-487.

• Mahalanobis, A. and Shah, J. (2014). A new guess-and-determine attack on the A5/1 stream cipher. Computer and Information Science 7(1).

• Mahalanobis, A. (2013). Are matrices useful in public-key cryptography? International Mathematical Forum 8(39):1939-1953.

• Mahalanobis, A. The MOR cryptosystem and extra-special p-groups. Proceedings of WCC 2012, Castro Urdiales, Spain July 9-13, 2012 & To appear in Journal of Discrete Mathematics and Cryptography.

• Mahalanobis, A. (2013). The automorphism group of the group of unitriangular matrices over a field. International Journal of Algebra 7(15):723-733.

• Maity, S., Arackaparambil, C. and Meyase, K. (2013). A new construction of resilient Boolean functions with high nonlinearity. Ars Combinatoria, 109:171-192.

• Mishra, R. (2013). Nodal Parity Invariant for knotted rigid vertex graphs. Journal of Knot Theory and its Ramifications. 22(4).

• Mishra, R. (2013). Polynomial unknotting and singularity index. Kyungpook Mathematical Journal. (Accepted for Publication).

• Hogadi, A. and Pisolkar, S. (2013). An equicharacteristic analogue of Hesselholt’s conjecture on cohomology of Witt vectors. Acta Arithmetica 158(2):165-171.

• Grobner, H. and Raghuram, A. (2013). On the arithmetic of Shalika models and the critical values of L-functions for GL(2n). With an appendix by Wee Teck Gan. American Journal of Mathematics (Accepted for Publication).

• Raghuram, A. Comparison results for certain periods of cusp forms on GL(2n) over a totally real number field. To appear in the Proceedings of the Legacy of Srinivasa Ramanujan conference, held in New Delhi in December 2012. (Accepted for Publication)

• Raghuram, A. (2013). Special values of the Riemann zeta function: some results and conjectures. To appear in the Proceedings of the workshop on Bloch-Kato conjecture for the Riemann zeta function for odd positive integers held at IISER Pune, July 2012. (Accepted for Publication)

• Biswas, I. and Sebastian, R. (2013). On rationality of moduli spaces of vector bundles on real Hirzebruch surfaces. Proceedings of Indian Academy of Sciences (Mathematical Sciences) 123:213-223.

• Sebastian, R. (2013). Smash nilpotent cycles on varieties dominated by products of curves. Compositio Mathematica, 149:1511-1518.

• Gates, Z., Singh, A., Ryan Vinroot, C. (2013). Strongly real classes in finite unitary groups of odd characteristic. Journal of Group Theory (Accepted for Publication).

• Bucur, A., Chantal, D., Feigon, B., Lalín, M. and Sinha, K. (2012). Distribution of zeta zeroes of Artin-Schreier covers. Mathematical Research Letters, 19:1329-1356.

Publications

Colloquia

• Prof Alladi Sitaram (ISI, Bangalore) February 13, 2014 Harish-Chandra; a mathematician's mathematician

• Prof Siddhartha Gadgil (IISc, Bangalore) December 18, 2013 Metric measure spaces and random matrices

• Prof Isha Dewan (ISI, Delhi) November 29, 2013 Competing risks model

• Prof Probal Chaudhuri (ISI, Kolkata) October 25, 2013 Deep inside data and distributions in dimensions one, two, three, ...., infinity

• Prof Neeraj Misra (IIT, Kanpur) October 9, 2013 Some monotonicity results for gamma distribution

• Prof Mythily Ramaswamy (TIFR-CAM, Bangalore) September 27, 2013 Optimal control problems

• Prof C S Seshadri (CMI, Chennai) September 20, 2013 Grassmann varieties

• Prof Rajeeva Karandikar (CMI, Chennai) September 18, 2013 Opinion polls in the context of Indian parliamentary democracy

• Prof Kapil Paranjape (IISER, Mohali) September 16, 2013 Real and complex multiplication lattices

• Prof Gadadhar Misra (IISc, Bangalore) September 13, 2013 The Bergman kernel

• Prof Adimurthi (TIFR-CAM, Bangalore) August 30, 2013 Structure of entropy solutions for conservation laws

• Prof Satyagopal Mandal (University of Kansas, Lawrence, USA) August 2, 2013 Inverting arrows and derived categories

• Prof Nikolai Vavilov (St. Petersburg State University) July 12, 2013 Decomposition of unipotents : Recent advances (alias Paghi Uno, Prendi Tre)

• Prof Dinesh Thakur (Arizona State University, USA) July 5, 2013 Special values of Gamma, Zeta functions and algebraic structures

• Prof Balasubramanian (IMSc, Chennai) March 15, 2013 Additive combinatorics

Special Talks

• Dr Anupam Singh (IISER, Pune) December 25, 2013 Classical groups and algebras with involution

• Prof Ivan A Panin (Petersburg Department of Steklov Institute of Mathematics) December 19, 2013 On a Grothendieck and Serre conjecture on principal G-bundles over regular local rings containing an infinite field

• Prof M S Raghunathan (IIT, Mumbai) December 18, 2013 Kneser-Tits Problem

• Prof M S Raghunathan (IIT, Mumbai) December 17, 2013 Kneser-Tits Problem

• Prof Dipendra Prasad (TIFR, Mumbai) December 16, 2013 Maximal subgroups of classical groups

• Prof G Lusztig (MIT, USA) December 16, 2013 Bruhat decomposition and conjugacy classes in classical groups

• Prof K N Raghavan (IMSc, Chennai) December 13, 2013 B-N pairs and Bruhat decomposition

• Dr Maneesh Thakur (ISI, Delhi) December 12, 2013

Colloquia & Seminars

On mod-2 invariants of G_2 and F_4 • Dr Debargha Banerjee (IISER, Pune) November 22, 2013

Modular Forms-A link road between numbers and geometry Algebra-Geometry Seminars

• Prof A J Parameswaran (TIFR, Mumbai) November 6, 2013 Construction of Grassmanian, Flag manifolds and Schubert subvarieties

• Prof S M Bhatwadekar (Bhaskaracharya Pratishthana, Pune) October 8, 2013 Projective modules and zero cycles

• Dr Nagaraj D S (IMSc, Chennai) September 17, 2013 Complex projective varieties

Analysis Seminars • Prof P N Srikanth (TIFR-CAM, Bangalore) March 4, 2014

Lecture 1: Regularity of Weak Solution; Lecture 2: Solutions concentrating on $S^1$ orbits • Prof M C Joshi (IIT, GN) February 25, 2014

Mathematical Perspective of Control Theory – A Glimpse • Prof Alladi Sitaram (ISI, Bangalore) February 11, 2014

Some generalizations of the Wiener-Tauberian theorem • Prof R Sakthivel (SRIT Coimbatore) January 10, 2014

Robust control for a class of uncertain dynamical systems • Dr Sheetal Dharmatti (IISER, Thiruvananthapuram) December 26, 2013

H infinity feedback boundary stabilization of two dimensional Navier Stokes' equation • Dr Sandeep (TIFR-CAM, Bangalore) November 28, 2013

Moser-Trudinger type inequalities • Dr Diganta Borah (IISER, Pune) November 21, 2013

Hartogs's extension phenomenon and domains of holomorphy • Ms Yasmeen Akhtar (IISER, Pune) November 7, 2013

The Riemann mapping theorem • Prof Venky Krishnan (TIFR-CAM, Bangalore) October 31, 2013

Microlocal analysis of transforms in synthetic aperture radar imaging

• Dr Chandrasheel Bhagwat (IISER, Pune) October 24, 2013 On Fourier transforms and Paley-Wiener theorems on real semisimple Lie groups

• Prof Ravi Aithal (University of Mumbai, Mumbai) October 17, 2013 Synge's Theorem

• Dr Anindya Goswami (IISER, Pune) October 3, 2013 Ito Integration and its martingale property

• Dr Anindya Goswami (IISER, Pune) September 26, 2013 Brownian motion and its differential generator

• Dr Anisa Chorwadwala (IISER, Pune) September 19, 2013 The maximum principles in differential equations-Lecture 3

• Dr Anisa Chorwadwala (IISER Pune) September 12, 2013 The Maximum principles in differential equations-Lecture 2

• Dr Anisa Chorwadwala (IISER Pune) September 5, 2013 The maximum principles in differential equations

Geometry Seminars • Prof S Senthamaraikannan (CMI, Chennai) April 12, 2013

Ring of invaraints under a finite group

• Prof S Senthamaraikannan (CMI, Chennai) April 11, 2013 Geometric invariant theory

• Prof S Senthamaraikannan (CMI, Chennai) April 10, 2013 Schubert varieties

• Prof Indranil Biswas (TIFR, Mumbai) September 10, 2013 A construction of a universal connection

• Dr Swagata Sarkar (ISI, Kolkata) March 22, 2013 Finite group actions on Kan complexes

Minor Thesis Seminars • Mr Sushil Bhunia (IISER, Pune) March 3, 2014

Whitehead graphs on handlebodies

• Mr Rohit Joshi (IISER, Pune) February 20, 2014 A theorem on analytic continuation of functions of several complex variables

• Ms Neha Prabhu (IISER, Pune) February 17, 2014 Ramanujan graphs

• Mr Jatin Majithia (IISER, Pune) February 10, 2014 Theory of rational option pricing

• Ms Yasmeen Akhtar (IISER, Pune) January 17, 2014 Characterisation of the unit ball in C^n by its automorphism group

Number Theory Seminars • Dr Chandrasheel Bhagwat (IISER, Pune) February 26, 2014

Siegel modular forms • Mr Punya Plaban Satpathy (IISER, Pune) February 19, 2014

Automorphic forms • Mr Mihir Sheth (IISER, Pune) February 12, 2014

Proof of the theorem of Iwasawa on the mu invariants. • Mr Mihir Sheth (IISER, Pune) February 5, 2014

A theorem of Iwasawa • Dr Baskar Balasubramanyam (IISER, Pune) January 28, 2014

A theorem of Matsushima and Shimura (without proof) that relates this space of cusp forms to cohomology of certain arithmetic groups

• Dr Baskar Balasubramanyam (IISER, Pune) January 22, 2014 Cusp forms w.r.t quaternion algebras over a totally real number field

Dr Debargha Banerjee (IISER, Pune) January 15, 2014 Cusps and Fourier expansions of Hilbert modular forms

• Dr Debargha Banerjee (IISER, Pune) January 8, 2014 Introduction to Hilbert Modular forms

• Prof A Raghuram (IISER, Pune) March 22, 2013 Number theory and cohomology

• Dr Kaneenika Sinha (IISER, Pune) Introduction to modular forms - 3 lectures

• Dr Vivek Mallick (IISER, Pune) Complex tori and elliptic curves - 2 lectures

• Dr Ronnie Sebastian (IISER, Pune) Riemann surface structure on quotients of the upper half plane and their genus - 2 lectures

• Dr Baskar Balasubramanyam (IISER, Pune) Hecke operators on modular forms - 1 lecture

• Dr Kaneenika Sinha (IISER, Pune) L-functions associated to modular forms - 1 lecture

Visitors’ Seminars • Dr Stefan Friedl (University of Regensburg, Germany) March 5, 2014

The geometrization theorem for 3-manifolds • Dr Shane D'Mello (TIFR, Mumbai) February 24, 2014

Chord diagrams and real rational planar quartics • Dr Jayanta Pal (IIT, Patna) February 10, 2014

Penalization based approach in the spiking problem for the estimation of shape restricted functions • Dr Arnab Mitra (Ben Gurion University, Israel) February 7, 2014

On ladder representations • Dr Saswata Shannigrahi (IIT, Guwahati) February 3, 2014

Two coloring uniform hypergraphs: bounds and algorithms • Prof Krishna B Athreya (Iowa State University, USA) January 27-30, 2014

Introduction to Markov chains and Brownian motion

• Dr Sumanta Sarkar (ISI, Kolkata) October 25, 2013 Constructions of cryptographically significant Boolean functions

• Dr Priyanka Shukla (IISER, Kolkata) September 30, 2013 Stability and pattern formation in rapid granular flows

• Dr Shodhan Rao (Groningen University, The Netherlands) September 25, 2013 A graph-theoretical approach to the analysis and model reduction of chemical reaction networks

• Prof C S Seshadri (CMI, Chennai) September 19, 2013 Jacobian varieties

• Mr Sugata Mondal (IMT, Toulouse, France) September 10, 2013 Hyperbolic surfaces with small eigenvalues

• Dr Dipramit Majumdar (ISI, Bangalore) September 6, 2013 Geometry of Eigencurve at critical Eisenstein series of weight 2

• Dr Sanjay Singh (TIFR, Mumbai) September 3, 2013 Holonomy group group scheme

• Dr Mousomi Bhakta (University of New England, Australia) August 21, 2013 Semi linear elliptic equations and the generalized boundary trace

• Dr Anup Biswas (University of Texas, Austin, USA) August 20, 2013 Law of large numbers for queues under earliest deadline first scheduling

• Dr Tejas Kalelkar (Washington University, St. Louis, USA) August 2, 2013 Taut foliations of punctured surface bundles

• Dr Sarang Sane (University of Kansas, USA) July 29, 2013 Projective module and various avatars of the Euler characteristic

• Mr Rohit Dilip Holkar July 18, 2013 Action groupoids and a remark on generalizing Gelfand Naimark theorem

• Ms Asha Sebastian (NIT, Calicut) July 12, 2013 Introductory knot theory

• Prof Dinesh Thakur (Arizona State University, USA) June 28, 2013 What should `e' and `pi' be, if `integers' are replaced by `polynomials'?

• Dr Atul A Dixit (Tulane University) May 30, 2013 Ramanujan-Hardy-Littlewood-Riesz phenomena and monotonicity results for Dirichlet L-functions

• Dr Ronnie Sebastian (ISI, Bangalore) March 26, 2013 Smash nilpotent cycles on varieties dominated by products of curves

• Dr Debraj Chakrabarti (TIFR-CAM, Bangalore) March 21, 2013 Holomorphic maps

• Dr Arnab Saha (Australian National University, Australia) March 15, 2013 Arithmetic jet spaces and Witt vectors

• Dr Amit Hogadi (TIFR, Mumbai) March 8, 2013 Fundamental groups of algebraic varieties

• Dr Supriya Pisolkar (TIFR, Mumbai) March 7, 2013 Commensurability and representation equivalent arithmetic lattices

• Dr Sachin Talathi (University of Florida, Gainesville, FL, USA), February 22, 2013 STDP induced synchrony in inhibitory neural networks: Theory and experiments

ATMW Workshop on Chevalley Groups

May 13-24, 2013 &

A Conference on Groups and Representations

May 24-26, 2013

AIS on Classical Groups and K-Theory December 5-26, 2013

AIS on Riemann Surfaces and Algebraic Curves June 3-22, 2013

Indian Women and Mathematics Symposium July 26-28, 2013

Trip to Lavasa

Traditional Day

At a Dinner & DJ Party

Group Picture taken during Vada-Pav Party

A Sweet-dish Potluck on Makarasankranti

Mathematics Day 2013 March 14

The 2013 Mathematics Day celebration included conducting a Mathematics Quiz Competition on the evening of March 13 which was open to all BSc, MSc, BS MS students from all over Pune. Many interesting activities were organized on March 14th such as the premiere of the movie "The Genius of Srinivasa Ramanujan" directed by Nandan Kudhyadi, co-produced by Vigyan Prasar and IISER Pune and featuring Prof A Raghuram; a skit by IISER members called "Life of π "; a colloquium by Prof Chandrashekhar Khare (FRS) from UCLA; a seminar by Dr Vivek Mallick; felicitation of Mathematics Olympiad winners; prize distributions for the quiz competition winners; release of various promotional accessories; and many more fun activities.

Indian Institute of Science Education and Research (IISER) Pune Dr Homi J Bhabha Road, Pashan, Pune – 411 008, Maharashtra, India Phone: +91 20 2590 8001 Fax: +91 20 2586 5315 Website: www.iiserpune.ac.in