Dr Mathew Pugh - PhD Cardiff
Telephone: +44(0)29 208 76862
Fax: +44(0)29 208 74199
My interests are in operator algebras, noncommutative geometry and mathematical physics. My work has revolved around the theory of modular invariant partition functions for SU(3) integrable statistical mechanical models and related subfactor constructions. The theory of alpha induction associates a modular invariant to a braided subfactor. My research to date has focused on braided subfactors associated to the SU(3) modular invariants. These modular invariants are labeled by a family of graphs, which we call SU(3) ADE graphs. These graphs are illustrated here, along with their 0-1 parts (in some cases these 0-1 parts appear as the principal graphs for certain subfactors) and also the McKay graphs, or representation graphs, for the exceptional finite subgroups of SU(3).
In particular I have studied various invariants associated with these SU(3) braided subfactors. This included the computation of Ocneanu cells for these graphs, which led to the realisation of the SU(3) modular invariants by braided subfactors. Another direction has been the formulation of A2-planar algebras which captures the structure contained in the subfactor double complex associated to the SU(3) ADE graphs and a description of certain modules over these A2-planar algebras. In another direction I have studied spectral measures for the SU(3) ADE graphs. More recently I have studied the almost Calabi-Yau algebras associated to these SU(3) ADE graphs, and determined certain homological invariants of these algebras.
Mathematical Physics (Operator Algebras Group)
Almost Calabi-Yau algebras associated to SU(3) modular invariant partition functions, QFT Seminar, Oxford University, January 2014
Almost Calabi-Yau algebras associated to SU(3) modular invariant partition functions, WIMCS-LMS Conference on Classifying Structures for Operator Algebras and Dynamical Systems, Aberystwyth, September 2013
Spectral Measures invariant under finite subgroups of GL(2,Z), WIMCS Workshop on Operator Algebras, April 2013
Almost Calabi-Yau algebras associated to SU(3) modular invariant partition functions, Joint Algebra and Analysis Seminar, Glasgow University, January 2013
Braided subfactors and conformal field theory I & II (2 talks), LMS Midlands Regional Meeting & Workshop on Quantum Probabilistic Symmetries, Aberystwyth, September 2012
On nimrep graphs associated to SU(3) modular invariant partition functions, Analysis Seminar, Newcastle University, May 2012
On nimrep graphs associated to SU(3) modular invariant partition functions, 2012 Wales Mathematics Colloquium, Gregynog, May 2012
On Almost Calabi-Yau Algebras associated to SU(3) Modular Invariant Partition Functions, INI-WIMCS Meeting on Noncommutative Geometry, Cardiff, April 2012
On Nimrep Graphs associated to SU(3) Modular Invariant Partition Functions, EU-NCG Fourth Annual Meeting, Bucharest, April 2011.
SU(3) Modular Invariant Partition Functions, WIMCS Annual Meeting- Mathematical Physics Cluster Session, Cardiff, December 2010.
A2-Planar algebras (2 talks), School on Planar Algebras, Cardiff, February 2010.
Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory, EU-NCG Second Annual Meeting and Midterm Review, Copenhagen, September 2009.
Co-organiser with David E Evans (Cardiff), Tim Porter (Bangor) of WIMCS Workshop on Higher Gauge Theory, TQFT's and Categorification at Cardiff, 9-10 May 2011
Co-organiser with David E Evans of a Learned Society of Wales, Frontiers Lecture at Cardiff, 17 January 2011
Co-organiser with David E Evans of EU-NCG Focused Semester on Mathematical Physics at Cardiff, February – June 2010
BSc – Cardiff University 2004
PhD – Cardiff University 2009
Thesis: "The Ising Model and Beyond"
Previous teaching: MA0322 Knots – 2008/09