Dr Mathew Pugh - PhD Cardiff
Overview
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Position:
Welsh Medium Lecturer
Email:
PughMJ@cardiff.ac.ukTelephone: +44(0)29 208 76862
Fax: +44(0)29 208 74199
Extension: 76862
Location: M/2.20
Research Interests
My interests are in operator algebras, noncommutative geometry and mathematical physics. My work has revolved around the theory of modular invariants for SU(3) integrable statistical mechanical models and related subfactor constructions. A family of graphs are associated to these modular invariants through the theory of alpha induction. These SU(3) ADE graphs have been the focus of my research to date.
In particular this has 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.
My recent work has been to study the almost Calabi-Yau algebras associated to these SU(3) ADE graphs, including the computation of the homology of these algebras.
Research Group
Mathematical Physics (Operator Algebras Group)
Recent Significant Publications
D.E. Evans, M. Pugh, On the homology of almost Calabi-Yau algebras associated to SU(3) modular invariants. arXiv:1111.3585 [math.KT]
D.E. Evans, M. Pugh, Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants, Proc. EU-NCG, to appear. arXiv:1110.4547 [math.OA]
(With D.E. Evans). The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants, Comm. Math. Phys., to appear. arXiv:1008.1003 (math.OA)
(With D.E. Evans). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3), Comm. Math. Phys. 301 (2011), 771–809. arXiv:1002.2348 (math.OA)
(With D.E. Evans). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory, Commun. Math. Phys. 295 (2010), 363–413. arXiv:0906.4314 (math.OA)
(With D.E. Evans). A2-Planar Algebras II: Planar Modules, J. Funct. Anal. 261 (2011), 1923-1954. arxiv:0906.4311 (math.OA).
(With D.E. Evans). A2-Planar Algebras I, Quantum Topol. 1 (2010), 321--377. arXiv:0906.4225 (math.OA)
(With D.E. Evans). SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants, Rev. Math. Phys. 21 (2009), 877–928. arXiv:0906.4252 (math.OA)
(With D.E. Evans). Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs, Münster J. Math. 2 (2009), 95–142. arXiv:0906.4307 (math.OA)
Personal Website
Publications
D.E. Evans, M. Pugh, On the homology of almost Calabi-Yau algebras associated to SU(3) modular invariants. arXiv:1111.3585 [math.KT]
D.E. Evans, M. Pugh, Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants, Proc. EU-NCG, to appear. arXiv:1110.4547 [math.OA]
(With D.E. Evans). The Nakayama automorphism of the almost Calabi-Yau algebras associated to
SU(3) modular invariants, Comm. Math. Phys., to appear. arXiv:1008.1003 (math.OA)
(With D.E. Evans). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3), Comm. Math. Phys. 301 (2011), 771–809. arXiv:1002.2348 (math.OA)
(With D.E. Evans). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory, Commun. Math. Phys. 295 (2010), 363–413. arXiv:0906.4314 (math.OA)
(With D.E. Evans). A2-Planar Algebras II: Planar Modules, J. Funct. Anal. 261 (2011), 1923-1954. arxiv:0906.4311 (math.OA).
(With D.E. Evans). A2-Planar Algebras I, Quantum Topol. 1 (2010), 321--377. arXiv:0906.4225 (math.OA)
(With D.E. Evans). SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants, Rev. Math. Phys. 21 (2009), 877–928. arXiv:0906.4252 (math.OA)
(With D.E. Evans). Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs, Münster J. Math. 2 (2009), 95–142. arXiv:0906.4307 (math.OA)
Research
Conference talks
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.
Research responsibilities
Local co-organiser with David E Evans and Otgonbayar Uuye of INI-WIMCS Meeting on Noncommutative Geometry at Cardiff, 16–20 April 2012.
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
Biography
BSc – Cardiff University 2004
PhD – Cardiff University 2009
Thesis: "The Ising Model and Beyond"
Previous teaching: MA0322 Knots – 2008/09