Symplectic geometry and Chern-Simons gauge theory

我的研究方向是辛几何。它涉及上同调中的不变量和等变上同调。 在某些情况下，它还涉及等变K-理论。 最重要的对象是辛商和超Kaehler商。一个基本问题是Kirwan的满足性，在 也就是说，自然映射是否从辛流形的等变上同调到辛流形的普通上同调 商是满足词。 研究的一个对象是基环群，它是余伴轨道的无限维类似物，它 产生于规范理论。我的研究涉及共轭空间，它是配备了反辛对合和的辛流形 与对合相容的哈密顿环面作用量。

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.