abstract: Jay Jorgenson and Serge Lang called the heat kernel “universal gadget which is a dominant factor practically everywhere in mathematics, also in physics, and has very simple and powerful properties”.
The main goal of this lecture series is to provide a complete construction of the heat kernel of an arbitrary Riemannian manifold, and, to establish its properties including the conservation property. Some cutting edge researches and important open conjectures will be discussed.
The audience is expected to know basic concepts in Analysis and that of Riemannian manifolds.