MATH 614: Topics in Analysis (Spring 2005)

Instructor: Laurent Saloff-Coste

Meeting Time & Room

Left-invariant sub-Laplacians on Lie groups: Heat kernel estimates and hypoellipticity.

In this course, I will try to give a self-contained proof of Hormander's celebrated theorem concerning the hypoellipticity of sums of squares of vector fields in the model case where the vector fields are left-invariant vector fields on a Lie group (for instance, on a compact Lie group).

I will attack this problem using the basic geometry of the metric balls associated to a Hormander family of vector fields and heat kernel estimates. These two subjects will be developed more or less from scratch. I will also discuss the use of the representation theory of compact groups in that context.

Last modified: October 7, 2004