Geometry, Algebra, Mathematical Physics and Topology Research Group

Our interests sweep a broad range of topics, from algebra, geometry, topology, including operator algebras, and non-commutative geometry in pure mathematics, to algebraic and conformal quantum field theory and integrable statistical mechanics in mathematical physics.

The main areas of research within the current group are:

Pure mathematics

  • Algebraic Geometry
  • DG categories and derived categories associated to algebraic varieties
  • Operator algebras and non-commutative geometry
  • Subfactors and planar algebras
  • Orbifolds and the McKay correspondence in Algebraic Geometry and Subfactor Theory
  • Categorification problems, Mirror symmetry, Moduli spaces
  • Quiver representations in Algebraic Geometry and Subfactor Theory
  • K-theory - including twisted and equivariant versions
  • Quantum symmetries: subfactors, tensor categories, Hopf algebras, quantum groups;
  • Enumerative Combinatorics.

Mathematical physics

  • Algebraic Quantum Field Theory
  • Conformal Field Theory
  • Statistical Mechanics: classical and quantum, integrable systems.

Head of Group

David E Evans Photograph

Professor David E Evans

Research Professor of Mathematics

Welsh speaking
Email:
evansde@cardiff.ac.uk
Telephone:
+44 (0)29 2087 4522

Academic staff

Dr Andreas Aasurad photograph

Dr Andreas Aaserud

Research Associate

Email:
aaseruda@cardiff.ac.uk
Telephone:
+44 (0)29 2087 0617
Photograph of Dr Roger Behrend

Dr Roger Behrend

Senior Lecturer

Email:
behrendr@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5543
Photograph of Dr Gandalf Lechner

Dr Gandalf Lechner

Lecturer

Email:
lechnerg@cardiff.ac.uk
Telephone:
+44(0)29 208 75553
Dr Timothy Logvinenko photograph

Dr Timothy Logvinenko

Lecturer

Email:
logvinenkot@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5546
Dr David McConnell photograph

Dr David McConnell

Lecturer

Email:
mcconnelld@cardiff.ac.uk
Telephone:
+44 (0)29 2088794
Ulrich Pennig photograph

Dr Ulrich Pennig

Lecturer

Email:
pennigu@cardiff.ac.uk
Telephone:
+44 (0)29 2068 8852
Photograph of Dr Mathew Pugh

Dr Mathew Pugh

Welsh Medium Lecturer

Welsh speaking
Email:
pughmj@cardiff.ac.uk
Telephone:
+44 (0)29 2087 6862
Dr Simon Wood photograpgh

Dr Simon Wood

Lecturer

Email:
woodsi@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5312

Current events

All seminars are held in Room M2.06 on Thursdays at 15:10 unless otherwise stated. All are welcome.

Programme organiser and contact: Dr Mathew Pugh

DateSpeakerSeminar

5 October 2017

Room M1.02

Gerard Watts (King's)

Conformal Field Theory defects - old and new

I will try to summarise some old and some new work on defects in two dimensional conformal field theory. Defects have played important roles from the Jordan-Wigner transformation onwards, but there are still interesting questions to ask and some hope that they can be answered.

Monday

16 October 2017

16:10-17:00

Rolf Gohm (Aberystwyth)

Star generators of S as a noncommutative exchangeable sequence

Gohm and Koestler developed an interpretation of Thoma's formula for extremal characters of S as a de Finetti type theorem. Here a basic observation is that the so-called star generators form a noncommutative exchangeable sequence. We discuss the method and explore its potential by looking at more general states for which this basic observation still holds.

26 October 2017

Paweł Dłotko (Swansea)

Practical problems, theory and computations: A few simple stories on topology in action

In this talk I will present a few problems in applied science that have been solved using methods from computational topology and in general computational mathematics. Starting from down-to-earth material science, via dynamical systems, ending up in brain research. I will present a feedback loop between theory and algorithms: how those two works together to solve problems, how they get mutual inspiration and why in applied sciences they should not be separated.

2 November 2017

Simon Wassermann (Glasgow)

Free groups and operator algebras

Wednesday 8 November 2017

 

Maths Colloquium

Speaker: Constantin Teleman (Oxford)

9 November 2017

Alexander Kasprzyk (Nottingham)

To be confirmed

23 November 2017

Ilke Canakci (Newcastle)

To be confirmed

30 November 2017

David Ridout (Melbourne)

To be confirmed

7 December 2017

Kazuya Kawasetsu (Melbourne)

To be confirmed

13-15 December 2017

 

LMS South Wales & South West Regional Meeting and Workshop on Algebraic Structures and Quantum Physics

Speakers include: Shahn Majid (Queen Mary), Ingo Runkel (Hamburg), Chris Fewster (York), Veronique Fisher (Bath), Christian Korff (Glasgow), Pieter Naaijkens (Aachen), Ulrich Pennig (Cardiff), Ko Sanders (Dublin), Anne Taormina (Durham), Michael Tuite (Galway)

8 February 2018

Dario Beraldo (Oxford)

To be confirmed

Programme organiser and contact: Dr Mathew Pugh

Past events

GAPT Seminars 2017-18

GAPT Seminars 2016-2017

GAPT Seminars 2015-2016

GAPT Seminars 2014-2015

GAPT Seminars 2013-2014

GAPT Seminars 2012-2013

GAPT Seminars 2011-2012

GAPT Seminars 2010-2011

GAPT Seminars 2009-2010

GAPT Seminars 2008-2009