Canada Research Chair in Differential Geometry and Topology

加拿大微分几何和拓扑研究主席

• 批准号: CRC-2014-00070
• 负责人: Lalonde, François
• 金额: $ 14.57万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=695505
• 关键词: Canada; Research; Chair; Differential; Geometry

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.

本主席旨在解决我们对开弦理论理解的主要差距之一。该理论有一个数学对应物，称为辛拓扑，它构成了我们主席的中心焦点。这两种理论同时出现，但各自独立，在 20 世纪 80 年代，弦理论作为一项伟大的事业，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，同时辛拓扑学也诞生了回应哈密顿力学的深层问题。主席设立了一个长期研究计划来填补这一空白，我们的集群理论迄今为止已经取得了重大成功。 本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：“当考虑与所考虑的粒子数量相关的各种限制时，辛理论的主要刚性特征在多大程度上持续存在。这个问题当人们为每个粒子分配一定程度的测量不确定性和排除原理时，就会变得令人着迷。