Canada Research Chair in Differential Geometry and Topology

这个教席的目的是解决我们对开弦理论理解中的一个主要空白。这一理论有一个数学上的对应物，称为辛拓扑学，它构成了我们主席的中心焦点。这两个理论同时但独立地出现在20世纪80年代的S，弦理论作为一项奇妙的事业，将量子理论(无穷小尺度)与广义相对论(大尺度)统一起来，这是爱因斯坦的梦想，而辛拓扑学是为了回应哈密顿力学的深层问题而诞生的。这位主席设立了一个长期研究计划来填补这一空白，我们的集群理论，到目前为止，已经取得了重大成功。*这位主席的另一个重点是寻找“统计辛拓扑”，它具体提出了这样一个问题：“当人们考虑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仍然存在。当人们为每个粒子分配其测量中的不确定程度和排除原则时，这个问题变得有趣起来。

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.