## Obstructions to the existence of conformally compact Einstein manifolds

Matthew Gursky (University of Notre Dame and Institute for Advanced Study, Princeton)

Title:  Obstructions to the existence of conformally compact Einstein manifolds

Abstract:   I will talk about a singular boundary value problem for Einstein metrics that arises in the Fefferman-Graham theory of conformal invariants and in the AdS/CFT correspondence.  I will describe an index-theoretic invariant which gives an obstruction to existence in the case of spin manifolds.  This is joint work with Q. Han and S. Stolz.  Since existence is obstructed, I will talk about recent work with R. Graham and G. Szekelyhidi on some related singular boundary value problems that are unobstructed.