2007-02-09

Laurent Saloff-Coste, Cornell University

The long time behavior of heat diffusion kernels on real connected Lie groups

A description of the results of N. Varopoulos

To each finite family of left invariant vector fields that generates the Lie algebra, we can associate a sub-Laplacian (the sum of the squares of these vector fields) and the corresponding heat kernel (a smooth positive function of time and space). Of interest to us in this talk is the long time behavior of the value of this function at the neutral element and how this long time behavior is related to the global geometry and the algebraic structure of the underlying group. I will describe what is known including a set of remarkable results obtained around 1995-2000 by my former advisor, N. Varopoulos.