# Obstructions to the existence of conformally compact Einstein manifolds

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In this talk I will describe a singular boundary value problem for Einstein metrics. This problem arises in the Fefferman-Graham theory of conformal invariants, and in the AdS/CFT correspondence. After giving a brief overview of some important results and examples, I will present a recent construction of boundary data which cannot admit a solution. Finally, I will introduce a more general 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.