What is... the heat kernel?

This page hosts information on Asilya Suleymanova's talk "What is … the heat kernel?" at the "What is …?" seminar. The talk will take place on Friday, June 19, 4:00pm at HU Berlin.

Abstract

First we will discuss the notion of a kernel of an operator and the heat operator itself. On the Euclidean space the scalar heat kernel is given by the exact formula . For an arbitrary Riemannian manifold it is usually impossible to find an exact expression for the heat kernel. However for many problems approximate solution suffices. For example, I will show how the local Atyiah-Singer index theorem can be proven using heat kernel approach.

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