Mathematical Sciences: Geometry of Loop Spaces and Groupoids

小行星9504522 主要主题的研究让-吕克Brylinski是几何的循环空间和空间的节点，其关系的拓扑和几何的有限维流形。 Brylinski是发展微分几何的gerbes和他们的高阶类似物，并适用gerbes的研究模空间，特征类，互惠法，和流形不变量。 Brylinski的研究计划侧重于拓扑学，几何学和数学物理学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学中的有用工具。 ***

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. ***