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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=694236
• 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.

该椅子旨在解决我们对开放弦理论的理解中的主要差距之一。该理论具有数学对应物，称为象征性拓扑，构成了我们主席的中心重点。这两种理论都同时出现，但是在1980年代独立地，弦理论是一家出色的企业，可以将量子理论（无限规模）与一般相对论（大规模）统一，即爱因斯坦的梦想，而象征性拓扑是出生的响应哈密顿力学的深层问题。该主席制定了一项长期研究计划，以填补这一空白，即我们的群集理论，直到现在为止取得了重大成功。 该椅子的另一个重点是寻找“统计符号拓扑”，该问题具体地提出了一个问题：“当人们认为与所考虑的粒子数量相关的各种限制时，符号理论的主要刚度特征在多大程度上持续存在。当一个人分配给每个粒子的不确定性水平和排除原则时，变得有趣。