In this talk I will use the AdS/CFT correspondence to study some of the most interesting puzzles of black holes. The singularity and the region near it can be probed by examining the analytic structure of certain finite-temperature gauge theory correlation functions. This structure turns out to be quite subtle, and contains some interesting surprises. The long-time behavior of the same correlators reveals a puzzle which constitutes a very precise formulation of the black hole information paradox. I will discuss a possible resolution of this problem involving a quantum sum over bulk geometries.

Institute for Advanced Study, Princeton