Cornell Math - MATH 614, Spring 2007

MATH 614: Heat Kernels on Lie Groups (Spring 2007)

Instructor: Laurent Saloff-Coste

Meeting Time & Room

This course will be devoted to the analysis and geometry of sub-Laplacian on Lie groups (sums of squares of left-invariant vector fields): We will discuss the definition and main properties of subelliptic geometry (invariant case), the construction of the heat semigroup and the heat kernel associated to a sub-Laplacian. If time permit, we will prove the hypoellipticity of sub-Laplacians that satisfy the Hormander condition (the defining vector fields generate the Lie algebra). The presentation will to a large extent be at an introductory level.