Mathematical Sciences: Geometry of Loop Spaces and Groupoids

9504522 Brylinski：Jean-Luc Brylinski研究的主要主题是环空间和纽结空间的几何，以及它与有限维流形的拓扑和几何的关系。Brylinski正在发展Gerbe及其高阶类似物的微分几何，并将Gerbe应用于模空间、特征类、互易定律和流形不变量的研究。布赖林斯基的研究计划集中在拓扑学、几何学和数学物理的最新进展之间令人兴奋的联系。布赖林斯基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许多用途，包括拓扑学、代数几何、微分几何和数论。它们也有望成为理论物理中的有用工具。***

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. ***