EVENT DETAILS AND ABSTRACT

Title: Topological and geometric aspects of the Laplace-Beltrami operator
Speaker: Austin Ford
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

I'll discuss the Laplace-Beltrami operator on compact manifolds and some standard PDEs associated to it, using this as an excuse to give an overview of some big theorems in microlocal analysis in special cases. I hope to discuss the Hodge decomposition theorem, the Duistermaat-Hörmander theorem on propagation of singularities for solutions to the wave equation, the Duistermaat-Guillemin trace theorem for the half-wave operator, and the Weyl law on growth of the spectrum for the Laplace-Beltrami operator. If there's time (which there won't be), I may say some things about what's known in other settings (noncompact manifolds, singular manifolds, etc.).