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
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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

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