Title: Pseudodifferential calculus for conformally compact manifolds
Abstract: Conformally compact manifolds possess a rich theory of elliptic differential operators. They play an important role in general relativity in the context of conformally compact Einstein manifolds, and as the basic setting for the AdS/CFT correspondence.
In this talk I'll approach the subject from the perspective of the pseudodifferential edge-calculus developed by Mazzeo & Melrose for manifolds with fibered boundary -- a powerful machine for handling PDEs in various exotic geometries. I'll introduce some basic concepts and motivating examples for the pseudodifferential calculus adapted to the geometry of conformally compact manifolds and discuss some applications to the study of Laplacians and other elliptic operators.
