Symplectic geometry and Chern-Simons gauge theory

辛几何和陈-西蒙斯规范理论

• 批准号: RGPIN-2016-05635
• 负责人: Jeffrey, Lisa
• 金额: $ 1.97万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=615815
• 关键词: Symplectic; geometry; Chern; Simons; gauge

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.

我的研究项目是辛几何。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凯勒商。一个基本问题是基尔万满射性，在 换句话说，是否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 商是满射的。 研究的一个对象是基环群，它是共交轨道的无限维模拟， 出现在规范理论中。我的研究涉及共轭空间，它是配备有反辛对合的辛流形，并且 与对合兼容的哈密顿环面作用。