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Geometry, Algebra, Mathematical Physics and Topology Research Group

In line with much of modern mathematics, this group is a blend of pure mathematicians and theoretical physicists.

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, quantum information theory, and integrable statistical mechanics in mathematical physics.

The main areas of research within the current group are:

Pure mathematics

  • Algebraic and enumerative combinatorics
  • Algebraic geometry
  • Braid group representations
  • Categorification problems, mirror symmetry, moduli spaces
  • DG categories and derived categories associated to algebraic varieties
  • K-theory - including twisted and equivariant versions
  • Modular tensor and fusion categories
  • Operator algebras and non-commutative geometry
  • Orbifolds and the McKay correspondence in Algebraic Geometry and Subfactor Theory
  • Quantum symmetries: subfactors, tensor categories, Hopf algebras, quantum groups
  • Quiver representations in Algebraic Geometry and Subfactor Theory
  • Subfactors and planar algebras.

Mathematical physics

  • Algebraic Quantum Field Theory
  • Conformal Field Theory
  • Quantum information
  • Statistical mechanics: classical and quantum, integrable systems
  • Topological phases of matter.

Head of Group

Professor Roger Behrend

Professor Roger Behrend

Professor

Email
behrendr@cardiff.ac.uk
Telephone
+44 (0)29 2087 5543

Academic staff

Professor David E Evans

Professor David E Evans

Honorary Distinguished Professor

Welsh speaking
Email
evansde@caerdydd.ac.uk
Dr Timothy Logvinenko

Dr Timothy Logvinenko

Reader

Email
logvinenkot@cardiff.ac.uk
Telephone
+44 (0)29 2087 5546
Dr Ulrich Pennig

Dr Ulrich Pennig

Senior Lecturer

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

Dr Mathew Pugh

Senior Lecturer

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

Dr Simon Wood

Senior Lecturer

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

Dr Pieter Naaijkens

Lecturer

Email
naaijkensp@cardiff.ac.uk
Telephone
+44 (0)29 2087 4522
Dr Manjil Saikia

Dr Manjil Saikia

Research Associate

Email
saikiam@cardiff.ac.uk
Professor George Elliott

Professor George Elliott

Honorary Visiting Professor

Dr Cian O'Brien

Dr Cian O'Brien

Lecturer

Email
obrienc13@cardiff.ac.uk
Telephone
+44 29208 74813

Postgraduate students