Symplectic geometry and Chern-Simons gauge theory

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My research program is in symplectic geometry. It involves invariants in cohomology and equivariant cohomology.***In some cases it also involves equivariant K-theory. *** ***Objects of fundamental importance are symplectic quotients and hyperkaehler quotients. One fundamental question is Kirwan surjectivity, in ***other words whether the natural map from the equivariant cohomology of a symplectic manifold to the ordinary cohomology of the symplectic ***quotient is surjective.*** ***One object studied is the based loop group, an infinite-dimensional analogue of a coadjoint orbit which ***arises in gauge theory. My research involves conjugation spaces, which are symplectic manifolds equipped with an antisymplectic involution and ***a Hamiltonian torus action compatible with the involution.**