**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).