Canada Research Chair in Geometry and Topology of Manifolds

加拿大流形几何与拓扑研究主席

• 批准号: CRC-2016-00234
• 负责人: Rochon, Frédéric
• 金额: $ 7.29万
• 依托单位: Université du Québec à 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=692651
• 关键词: Canada; Research; Chair; Geometry; Topology

Singularities are omnipresent in the sciences and in everyday life, from breaking waves to the notion of black holes in Einstein's theory of relativity. Mathematics, more specifically geometry, provides the right language to describe and study them. This Canada Research Chair will focus on developing and using analytic tools to study the geometry and topology of singular spaces. Among them, spectral invariants are especially useful as they allow us to `hear' the shape of a singularity. The proposed research program has many implications for the geometry and topology of smooth varieties, as they can be decomposed into simpler singular pieces.

奇点在科学和日常生活中无处不在，从破浪到爱因斯坦相对论中的黑洞概念。数学，更具体地说是几何，提供了正确的语言来描述和研究它们。这个加拿大研究教席将专注于开发和使用分析工具来研究奇异空间的几何和拓扑。其中，光谱不变量特别有用，因为它们允许我们‘听到’奇点的形状。所提出的研究方案对光滑簇的几何和拓扑学有许多启示，因为它们可以分解成更简单的奇异片段。