Megumi Harada
Profile Photo
Professor and Canada Research Chair
HH 325
(905) 525 9140 ext. 23432
(905) 522-0935

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

ArtsSci 1D06

ArtsSci 1D06

ArtsSci 1D06

On Research Leave

ArtsSci 1D06

Math 1C03
Math 2R03

Math 1C03
Math 3EE3

Math 3CY3
Math 3EE3
Math 701

On Research Leave

On Research Leave

Currently Supervising:
Büşra Atar (MSc Math)
Adrian Cook (MSc Math)
Runyue Wang (MSc Math)

Past Students:
Lauren DeDieu (PhD Math)
Julia Gibson (MSc Math)
Tatsuya Horiguchi (Visiting Student)
Jarvis Kennedy (MSc Math)
Maryam Nowroozi (MSc Math) 

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