Mathematical Sciences: Geometry of Loop Spaces and Groupoids

数学科学：循环空间和群形的几何

• 批准号: 9504522
• 负责人: Jean-Luc Brylinski
• 金额: $ 13.62万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1998-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504522&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Loop; Spaces

9504522 Brylinski The main theme of the research of Jean-Luc Brylinski is the geometry of loop spaces and of the space of knots, and its relation with the topology and geometry of finite-dimensional manifolds. Brylinski is developing the differential geometry of gerbes and their higher order analogues and is applying gerbes to the study of moduli spaces, of characteristic classes, of reciprocity laws, and of manifold invariants. The research program of Brylinski focuses on the exciting connections between topology, geometry and recent progress in mathematical physics. Brylinski will continue to explore the mathematical structures underlying these connections. These structures have many uses in several areas of mathematics, including topology, algebraic geometry, differential geometry and number theory. They are expected to be useful tools in theoretical physics as well. ***

Jean-Luc Brylinski的主要研究主题是环空间和结点空间的几何，以及它们与有限维流形的拓扑和几何的关系。Brylinski正在发展gerbes及其高阶类似物的微分几何，并将gerbes应用于模空间、特征类、互易律和流形不变量的研究。Brylinski的研究项目侧重于拓扑、几何和数学物理最新进展之间令人兴奋的联系。Brylinski将继续探索这些联系背后的数学结构。这些结构在数学的几个领域有很多用途，包括拓扑、代数几何、微分几何和数论。它们也有望成为理论物理的有用工具。＊＊＊