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.
Events
Current events
For an up-to-date programme of online talks, please see our calendar of events.
Previous years
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
Next steps
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.
Postgraduate research
Our research degrees give the opportunity to investigate a specific topic in depth among field-leading researchers.
Our research impact
Our research case studies highlight some of the areas where we deliver positive research impact.