Rafe Mazzeo

Abstract:   Asymptotically hyperbolic Einstein metrics have been studied intensively over the past several years, partly because of their connection with physics, but also because they provide a variety of interesting geometric and analytic challenges. I shall discuss some of the main analytic, geometric and topological goals of this theory and survey recent progress in this field, much of which centers on finding such metrics with prescribed `conformal infinities'. My main focus will be on the problem of filling compact scalar-positive 3-manifolds with metrics of this type, and I will describe recent joint work with Michael Singer which (almost) settles this, and which ultimately reduces to understanding the geometry of resolutions of isolated orbifold singularities in C².