# Harada, Megumi

Professor, Ph.D. (Berkeley)

Canada Research Chair

Dept. of Mathematics & Statistics, McMaster University

1280 Main Street West

Hamilton, Ontario,

Canada L8S 4K1

905-525-9140, **ext. 23432**

905-522-0935 (fax)

Megumi.Harada@math.mcmaster.ca**Office:** **HH/325**

Website: http://www.math.mcmaster.ca/Megumi.Harada

## Research

**Research Area:** Geometry & Topology

**Research Profile:** *Geometry and Topology*My research is in symplectic and hyperkahler geometry. 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.