Eric Bahuaud, Seattle University

Title: Geometrically Finite Asymptotically Hyperbolic Einstein metrics

Abstract: Asymptotically hyperbolic Einstein metrics are important in conformal geometry
and the physics of the AdS-CFT correspondence. In 1991, Graham and Lee proved that any
sufficiently small perturbation (in Holder norm) of the round metric on the unit sphere (with
dimension at least 3) is the "conformal infinity" of an asymptotically hyperbolic Einstein
metric on the open unit ball. In this talk I will give the background and explain the proof of
this result, and then discuss recent joint work with Rochon proving the existence of Einstein
metrics near certain geometrically finite quotients of the hyperbolic metric.