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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.

Research

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.

Meet the team

No picture for Declan Bays

Declan Bays

Research student

Email
BaysD@cardiff.ac.uk
Picture of James Binnie

James Binnie

Research Student/Graduate Tutor

Email
BinnieJA@cardiff.ac.uk
Picture of Diego Corro Tapia

Dr Diego Corro Tapia

Post-Doctoral Fellowship Researcher

Email
CorroTapiaD@cardiff.ac.uk
Picture of David Evans

Professor David Evans

Honorary Distinguished Professor

Email
EvansDE@cardiff.ac.uk
Picture of Shauna Ford

Miss Shauna Ford

Teaching Associate / Research Student

Email
FordS6@cardiff.ac.uk
No picture for Roman Gonin

Dr Roman Gonin

Research Associate

Email
GoninR@cardiff.ac.uk
No picture for Samuel Hannah

Samuel Hannah

Teaching Associate

Email
HannahS@cardiff.ac.uk
Picture of John Harvey

Dr John Harvey

Lecturer in Mathematical Sciences

Telephone
+44 29208 70943
Email
HarveyJ13@cardiff.ac.uk
No picture for Jamal Shafiq

Mr Jamal Shafiq

Research student

Email
ShafiqJN@cardiff.ac.uk
Picture of Ambrose Yim

Ambrose Yim

Post-doctoral Research Associate

Next steps

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Research that matters

Our research makes a difference to people’s lives as we work across disciplines to tackle major challenges facing society, the economy and our environment.

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Postgraduate research

Our research degrees give the opportunity to investigate a specific topic in depth among field-leading researchers.

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Our research impact

Our research case studies highlight some of the areas where we deliver positive research impact.