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.
