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
Picture of Gandalf Lechner

Dr Gandalf Lechner

Senior Lecturer

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

Dr Timothy Logvinenko

Senior 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

Senior 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 Ulrich Pennig.

DateSpeakerSeminar

31 January 2019

Vincenzo Morinelli (Tor Vergata, Rome)

To be announced.

13 December 2018

Ashley Montanaro (Bristol)

To be announced.

6 December 2018

Matthew Buican (Queen Mary, London)

To be announced.

15 November 2018

Vladimir Dotsenko (Trinity College Dublin)

To be announced.

18 October 2018

Paul Mitchener (Sheffield)

Categories of Unbounded Operators

The Gelfand-Naimark theorem on C*-algebras, which asserts that a C*-algebra, defined axiomatically, is the same thing as a closed sub-algebra of the algebra of bounded linear operators on a Hilbert space, is well-known. Of course, in some cases, for example, mathematical physics, the concern is with unbounded operators such as position and momentum in quantum mechanics.

In this talk, we explore a set of axioms for a mathematical object analogous to a C*-algebra, but for unbounded operators. In particular, our axioms are such that an analogue of the Gelfand-Naimark theorem holds.

11 October 2018

Fabian Hebestreit (Bonn / INI Cambridge)

Twisted K-theory via retractive symmetric spectra joint with Steffen Sagave

Twisted K-theory was originally invented to serve as the K-theoretic analogue of singular (co)homology with local coefficients and by design gives explicit Thom- and Poincaré duality isomorphisms. In this formulation it admits a direct description in terms of KK-theory of certain section algebras and thus has tight connections for instance to the geometry of scalar curvature. Modern homotopy theory on the other hand provides a universally twisted companion for every coherently multiplicative cohomology theory by means of parametrised spectra. This construction has very appealing formal properties and, indeed, applied to K-theory allows for much more general twists than those afforded by the operator algebraic one. Necessarily then, such twisted companions are defined in a much more formal manner and thus in general not easily tied to geometry.

The goal of my talk is to briefly explain the category of the title, that naturally houses both constructions and then sketch that, indeed, a suitable restriction of the universal one reproduces the operator theoretic version of twisted K-theory. Time permitting, I shall also sketch how our work strengthens recent results of Dardalat and Pennig, describing the more exotic twists of K-theory via self-absorbing C*-algebras.

4 October 2018

Stuart White (Glasgow)

Classification of simple nuclear C*-algebras

Recent years have seen repeated striking progress in the structure and classification of simple nuclear C*-algebras. I’ll try and survey what the state of the art is, focusing on recent developments. I’ll try and keep the talk self contained, starting out with what these `simple nuclear C*-algebras’ are and why anyone wants to classify them anyway.

28 June 2018

Lorenzo De Biase (Cardiff)

Generalised braid categorification

Ordinary braid group Brn is a well-known algebraic structure which encodes configurations of n non-touching strands (“braids”) up to continuous transformations (“isotopies”). A classical result of Khovanov and Thomas states that this group acts categorically on the space Fln of complete flags in Cn. Generalised braids are the braids whose strands are allowed to touch in a certain way. They have multiple endpoint configurations and can be non-invertible, thus forming a category rather than a group. In this talk I will present  some progress that have been made towards extending the result of Khovanov and Thomas to the categorification of the generalised braid category.

Previous years

GAPT Seminars 2017-2018

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