Mathematical Physics Cluster Research interests include: Aberystwyth University Institute of...
If you can't read please download the document
Mathematical Physics Cluster Research interests include: Aberystwyth University Institute of Mathematics and Physics Operator algebras and K-theory Quantum
Mathematical Physics Cluster Research interests include:
Aberystwyth University Institute of Mathematics and Physics
Operator algebras and K-theory Quantum Control Theory Quantum
Probability Quantum Computing Cardiff University School of
Mathematics Operator algebras and non-commutative geometry
K-theory, non-commutative dynamical systems. Quantum symmetries:
subfactors, tensor categories, Hopf algebras, quantum groups,
planar algebras Enumerative Combinatorics Modular invariants
Cardiff University School of Mathematics Foundations and
constructive approaches to Quantum Field Theory: algebraic
approach, conformal field theories including boundaries, curved
backgrounds, perturbation theory, topological field theories.
Classical general relativity: asymptotic charges, Hamiltonian
formalism, black holes, AdS/CFT. Statistical Mechanics: classical
and quantum, equilibrium and non-equilibrium, integrable systems
Swansea University Department of Mathematics, School of Physical
Sciences Quantum Algebra, Hopf algebras, quantum groups
Non-commutative differential geometry, Computability of physical
and mathematical systems, Categories and non-associative structures
Co-rings and comodules Homological algebra, triangulated categories
Swansea University Department of Physics, School of Physical
Sciences Quantum Field Theory, Cosmology String Theory Gauge-string
correspondence AdS/CFT strong-coupling dynamics of supersymmetric
gauge theory Phenomenology beyond the Standard Model Lattice Gauge
Field Theory Symmetry and Independence in Quantum Probability
Strongly coupled dynamics of quantum field theories Motivation and
Aim Development of a quantized theory of distributional symmetries
and invariance principles Investigation of quantized counterparts
of conditional independence in quantum probability Identification
of asymptotic models for scaling limits of interacting quantum
dynamical systems Future Cluster Activities Dr Claus Kstler,
Institute of Math and Physics, Aberystwyth Dr Carlos Nunez,
Department of Physics, Swansea Sefydliad Gwyddorau Cyfrifiadurol a
Mathemategol Cymru SGCMC WIMCS Wales Institute of Mathematical and
Computational Sciences Selected Cluster Activities Motivation and
Aim To develop and exploit techniques to investigate the strongly
coupled dynamics of quantum field theories (QFTs) Large N at
Swansea Swansea University, July 7-10 2009 A conference drawing
together the world's experts to discuss recent advances in strong
coupling dynamics in large N gauge theories. Speakers inlcuded:
Thomas Appelquist (Yale), Lawrence Yaffe (Seattle), Mikhail Shifman
(Minnesota), Cardiff Semester on Noncommutative Geometry and
Physics, February July 2010 Organized by David E Evans (Cardiff)
Long term visitors as well as a series of short term events, with
120+ participants in all, including: WIMCS MP Colloquium, 26
February 2010 held at Swansea Computer Science Speakers: Marcos
Mario (Geneva), Richard Thomas (Imperial) Planar Period Cardiff
University, 15 February 5 March 2010 Speakers included: S Bigelow
(UCSB), J Fuchs (Karlstad), Method To use the fact that certain
QFTs are known to have a dual description involving an emergent
higher dimensional gravitational theory. In particular, the strong
coupling regime of the QFT maps to the classical regime of the dual
gravitational theory and many observables can be calculated
exactly. To exploit the fact that the dual gravitational theory is
described beyond the classical regime by a QFT in order to
understand quantum gravitational effects. To discretize the QFT by
defining it on a spacetime Lattice in order that the functional
integral can be calculated numerically on state-of-the-art
computers by Monte Carlo techniques. Outcome The group has produced
new strong coupling results in QFTs with minimal and extended
supersymmetry. The results apply not only in the zero temperature
theory, but also at finite temperature and density (important for
heavy ion collisions and also in the early universe). The
observables which have been investigated include the spectrum of
states and their interactions, the expectation values of important
operators. The group has used these results to formulate new
dualities involving some QFTs which may have direct relevance in
the interpretation of experimental observation at the Large Hadron
Collider. Quantum field theory on curved space-times and curved
target-spaces Erwin-Schrodinger Institute, Vienna, March+April
2010, organized by Stefan Hollands (Cardiff) Frontiers Lecture of
the Learned Society of Wales Cardiff University, 17 January 2011
Speaker: Sir Michael Atiyah (Edinburgh) David E Evans (Cardiff) EU
Research Training Network in Noncommutative Geometry Appointments
in 2011: Method Systematic quantization of classical probability
using the language of operator algebras Investigate to which extent
classical de Finetti type results transfer to the quantum world
Investigate the relation of symmetry and independence in the
general quantized setting Selected Results - indicate deep
connections between important areas in modern analysis and its
applications. Noncommutative extended de Finetti theorem:
'exchangeability' and 'spreadability imply 'noncommutative
conditional independence' in terms of 'commuting squares' Failure
of common folklore facts from classical probability:
exchangeability' and 'spreadability of an infinite sequence of
random variables are no longer equivalent in the quantized setting.
Braided extended de Finetti theorem: we introduce 'braidability' as
a new symmetry intermediate to 'exchangeability and
'spreadability'. It applies to subfactor inclusions with small
Jones index Selected Publications R. Gohm; C. Kstler.
Noncommutative independence from the braid group B . Comm. Math.
Phys. 289 (2009), 435482. R. Gohm; C. Kstler. Noncommutative
independence from characters of the infinite symmetric group S .
arXiv:1005.5726 [math.OA] (2010). C. Kstler. A noncommutative
extended de Finetti theorem. J. Funct. Anal. 258 (2010), 10731120.
C. Kstler; R. Speicher. A noncommutative de Finetti theorem:
invariance under quantum permutations is equivalent to freeness
with amalgamation. Comm. Math. Phys. 291 (2009), 473490. Claus
Kstler, Institute of Math and Physics, AberystwythCarlos Nunez,
Department of Physics, Swansea Stefan Hollands (Cardiff) ERC
Starter Research Grant 2011-16 INI-WIMCS follow up meeting to Isaac
Newton Institute 2006 programme on Noncommutative Geometry to be
held at Cardiff or Gregynog in 2012 - application pending
Organizers David E Evans (Cardiff ), Nigel Higson (Penn State),
Shahn Majid (Queen Mary, London) Themes of meeting include:
Noncommutative Algebraic Geometry Representation Theory aspects of
Baum-Connes Free aspects of Noncommutative Geometry Noncommutative
Geometry and Conformal Field Theory Noncommutative Geometry and
Categorification Noncommutative Spacetime and Cosmology The
Standard Model and Beyond London Mathematical Society Spitalfields
Day Cardiff University, 17 May 2010. Speakers: Nigel Higson (Penn
State), Terry Gannon (Alberta) London Mathematical Society Regional
Meeting and Workshop Operator Algebras and Physics, Cardiff
University, 21-25 June 2010. Series of lectures by Constantin
Teleman and other speakers included Werner Nahm (Dublin) Annual
Meeting of the EU Research Training Network in Noncommutative
Geometry, Cardiff University, 28 June 2 July 2010 Speakers
included: J Mickelsson (Helsinki), Y Kawahigashi (Tokyo), A
Verbeure (Leuven), J Yngvason (ESI Vienna), . First Frontiers
Lecture of the Learned Society of Wales Cardiff University, 28 June
2010 Speaker: Dan Voiculescu (Berkeley) Collaborators include: Juan
Maldacena (IAS), Daniel Freedman (MIT) Alfonso Ramallo (Santiago de
Compostela), Nick Dorey (Cambridge) Kostas Skenderis (Amsterdam),
Dario Martelli (King's College) Free de Finetti theorem: quantum
exchangeability' yields a beautiful characterization of freeness
with amalgamation. This quantum probabilistic symmetry comes from a
compact quantum group. Thoma theorem is a quantum de Finetti
theorem: we give a new operator algebraic proof of the
characterization of extremal characters of the infinite symmetric
group. Alin Galatan (Bucharest) Antti Harju (Helsinki) Grace
Kennedy (UCSB) Jennifer Maier (Hamburg) Makoto Yamashita (Tokyo)
Provide new computational methods for exactly solvable models in
quantum statistical physics Application of the developed tools to
collective quantum effects, quantum control and information