The Mathematical and Computational Sciences at Western are represented by four separate departments: Applied Mathematics, Computer Science, Mathematics, and Statistical & Actuarial Sciences. The Department of Mathematics has established research groups in several areas of contemporary mathematics including algebra, analysis and analytic geometry, homotopy theory, and noncommutative geometry.
Each week the Department of Mathematics hosts a wide variety of seminars and events. For a comprehensive list of events, please consult our departmental calendar.
The starting point for the heat equation proof of the Atiyah-Singer index theorem is the celebrated McKean-Singer formula and the asymptotic expansion of the heat kernel. In this first lecture the following topics will be covered: basic Sobolev space theory, including Garding's inequality; finiteness and regularity results for elliptic PDE's on compact manifolds, Hodge decomposition theorem for elliptic complexes, existence of the heat kernel and its asymptotic expansion.