I work in the fields of geometry and topology, and my research deals with problems (loosely) motivated by mathematical physics.  More specifically, I’m interested in: Lie groups, equivariant cohomology theories, the geometry and topology of moduli spaces, symplectic geometry and hamiltonian actions, topological quantum field theories.

Here are some projects I have worked on:

Moduli spaces of vector bundles over real curves

Moduli spaces of vector bundles over a real curve: Z/2-Betti numbers

Classifying spaces of twisted loop groups

Cohomology of the moduli space of rank two vector bundles over a real curve

Deformation K-theory of groups (with Dan Ramras)

Smooth approximation in algebraic sets and the topological Atiyah-Segal map

Topology of moduli spaces of flat connections over a non-orientable surface

GKM-sheaves and non-orientable surface group actions

Antiperfection of Yang-Mills Morse theory over a non-orientable surface

Moduli of flat SU(3)-bundles over a Klein bottle

The moduli space of flat SU(2)-bundles over a nonorientable surface

Commuting n-tuples (with Lisa Jeffrey and Paul Selick)

The space of commuting n-tuples in SU(2)

Cohomology of the space of commuting n-tuples in a compact Lie group

Hamiltonian actions on generalized complex manifolds (with Yi Lin)

Generalized complex hamiltonian torus actions: Examples and constraints

Topology of generalized complex quotients