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.