Speaker: Andrew Raich (Arkansas)
Title: Analysis and Geometry in Several Complex Variables
Abstract: In this talk, I will start by reviewing the Laplacian on R^n and two of its most well known estimates that showcase “elliptic regularity”. From there, I’ll pivot to the complex Laplacian (called the d-bar Neumann Laplacian) and boundary complex Laplacian (called the Kohn Laplacian) and discuss how and why elliptic regularity fails. It turns out that neither operator ever satisfies elliptic estimates, and the estimates that the operators do satisfy depend on the geometry of the domain, namely, the curvature as measured by the Levi form. I will try to make this talk accessible to everyone.
