Geometry, Algebra, Mathematical Physics and Topology: GAPT
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 and Integrable Statistical Mechanics in Mathematical Physics.
Key Current Research Areas
Pure Mathematics
Algebraic Geometry
DG categories and derived categories associated to algebraic varieties
Operator algebras and non-commutative geometry
Subfactors and planar algebras
Orbifolds and the McKay correspondence in Algebraic Geometry and Subfactor Theory
Categorification problems, Mirror symmetry, Moduli spaces
Quiver representations in Algebraic Geometry and Subfactor Theory
K-theory - including twisted and equivariant versions
Quantum symmetries: subfactors, tensor categories, Hopf algebras, quantum groups;
Enumerative Combinatorics
Mathematical Physics
Algebraic Quantum Field Theory
Conformal Field Theory
Statistical Mechanics: classical and quantum, integrable systems
