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.