Symplectic geometry and Chern-Simons gauge theory

我的研究方向是辛几何。它涉及上同调和等变上同调中的不变量。 在某些情况下，它还涉及等变K理论。 最重要的对象是辛代数和超凯勒代数。一个基本问题是Kirwan满射性， 换句话说，从辛流形的等变上同调到辛流形的普通上同调的自然映射是否 商是满射的。 研究的一个对象是基环群，它是余伴随轨道的无限维模拟， 产生于规范理论。我的研究涉及共轭空间，这是辛流形配备了反辛对合， 与对合相容的哈密顿环面作用。

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.