Canada Research Chair In Differential Geometry And Topology

本讲座旨在解决我们对开放弦理论理解中的一个主要空白。这个理论有一个数学上的对应，叫做辛拓扑，它构成了我们讲座的中心焦点。这两种理论同时出现，但各自独立，在20世纪80年代，弦理论作为一项奇妙的事业，将量子理论（无限小尺度）与广义相对论（大尺度）统一起来，这是爱因斯坦的梦想，而辛拓扑学则是为了回应哈密顿力学的深层问题而诞生的。这个主席设立了一个长期的研究项目来填补这个空白，我们的集群理论，到目前为止，已经取得了重大的成功。这个主席的另一个重点是寻找“统计辛拓扑”，它具体地提出了这样一个问题：“当一个人考虑到与所考虑的粒子数量有关的各种限制时，辛理论的主要刚性特征在多大程度上持续存在？”当人们赋予每个粒子一定程度的测量不确定性和不相容原理时，这个问题就变得有趣了。

This Chair aims at resolving one of the major gaps in our understanding of Open String theory. This theory has a mathematical counterpart, called Symplectic Topology, that constitutes the central focus of our Chair. Both of these theories appeared at the same time, but independently, in the 1980's, String Theory as a fantastic enterprise to unify the Quantum theory (infinitesimal scale) with General relativity (large scale), the dream of Einstein, while Symplectic Topology was born in response to deep problems of Hamiltonian mechanics. This Chair set up a long term research program to fill this gap, our Cluster Theory that has had, up to now, major successes. The other focus of this Chair is the search for "Statistical Symplectic Topology", which concretely asks the question: "To which extent do the main rigidity features of Symplectic theory persist when one considers various limits related to the number of particles considered. This question becomes fascinating when one assigns to each particle a level of uncertainty in its measure and a principle of exclusion.