Date & Time: Friday, April 01, 2016, 15:30-17:30
Venue: Room No. 216

Title: Asymptotic expansion of the Heat Kernel

Speaker: Ritwik Mukherjee, School of Mathematics, TIFR Mumbai

Abstract: In this lecture we will first revisit Hodge theory from the point of view of the Heat equation. In particular, we will see how to prove the Hodge theorem by assuming the existence of the Heat Kernel. We will then look at the asymptotic expansion of the Heat Kernel and see how it leads to the signature theorem. In particular we will see how both the Hodge theorem and the signature theorem are special cases of the general statement "Analytical Index = Topological Index" (which is basically the statement of the Atiyah Singer Index Theorem).