Canada Research Chair in Differential Geometry and Topology

这张椅子旨在解决我们对开弦理论的理解中的一个主要差距。这个理论有一个数学对应物，称为辛拓扑，构成了我们主席的中心焦点。这两个理论同时出现，但独立，在20世纪80年代，弦论作为一个梦幻般的企业统一量子理论（无穷小尺度）与广义相对论（大尺度），爱因斯坦的梦想，而辛拓扑诞生于汉密尔顿力学的深层问题。这把椅子建立了一个长期的研究计划，以填补这一空白，我们的集群理论，有，到现在为止，重大的成功。 这把椅子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：“在何种程度上辛理论的主要刚性特征坚持当一个人考虑与所考虑的粒子数量有关的各种限制。当我们给每个粒子分配一个测量的不确定性水平和一个不相容原理时，这个问题就变得很有趣了。

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.