Microlocal Category

获奖：DMS 1105832，首席研究员：Dmitry tamarkin这些研究项目集中在与辛流形相关的范畴的微局部方法相关的问题，如Fukaya范畴。预计通过应用代数工具，如微分分级类别和更高类别，将通过避免横向性和其他难以提供的几何条件而产生几何简化。辛几何是对经典力学哈密顿版本的背景结构的研究。这类几何的研究在20世纪80年代发生了革命性的变化，因为使用了将曲面映射为辛流形的解析技术，这种观点导致了下面引用的深谷分类。这些深谷范畴携带了很多关于潜在辛流形的重要信息，如果对它们有一个比原始定义更不微妙的描述将会很有用。

AbstractAward: DMS 1105832, Principal Investigator: Dmitry TamarkinThese research projects concentrate on issues related to the microlocal approach to categories associated with symplectic manifolds, such as the Fukaya category. It is anticipated that by applying algebraic tools such as differential graded categories and higher categories, will yield geometric simplifications by avoiding transversality and other geometric conditions that can be hard to provide.Symplectic geometry is the study of the background structure for the Hamiltonian version of classical mechanics. The study of this kind of geometry was revolutionized in the 1980s by the use of analytic techniques involving maps of surfaces into symplectic manifolds, a point of view that led more recently to the Fukaya categories invoked below. These Fukaya categories carry a lot of significant information about the underlying symplectic manifold, and it would be useful to have a less subtle description of them than the original definition.