Mathematical Sciences: Geometry of Loop Spaces and Groupoids

点击翻译按钮获取中文摘要

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. ***