Research Area: Geometry & Topology

Research Profile: Geometry and Topology 
More specifically, I compute topological invariants, such as equivariant cohomology theories, of spaces with such structure. Symplectic geometry is the mathematical framework of classical physics; hyperkahler manifolds are symplectic manifolds wiht extra structure, are of particular recent interest due to their connections to theoretical physics. I am mainly concerned with the theory of symmetries of manifolds with these structures, as encoded by a Hamiltonian Lie group action, i.e. there exists a moment map on M encoding the action by Hamiltonian flows. Such group actions on symplectic and hyperkahler manifolds arise naturally in the context of physics, representation theory, and algebraic geometry. To a Hamiltonian space, one associates a symplectic (hyperkahler) quotient, which inherits a symplectic (hyperkahler) structure from the original manifold. The main theme of my recent research is the study of the topology and equivariant topology of these quotients, in particular the computation of their cohomology and complex K-theory rings.

Symplectic geometry, algebraic geometry

2021/2022
ArtsSci 1D06

2020/2021
ArtsSci 1D06

2019/2020
On Research Leave

2018/2019
ArtsSci 1D06

2017/2018
Math 1C03
Math 2R03

2016/2017
Math 1C03
Math 3EE3

2015/2016
Math 3CY3
Math 3EE3
Math 701

2014/2015
On Research Leave

2013/2014
On Research Leave