**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

**2022/2023**

ArtsSci 1D06

**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