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Black Holes, Holography and Quantum Gravity in Three Dimensions

The AdS/CFT correspondence is a powerful tool in the study of quantum gravity.  For gravity in 2+1 dimensions this duality can be made quite precise: it relates AdS quantum gravity to solvable conformal field theories, such as the one which governs the critical point of the 2d Ising model. This allows us to address basic questions about the landscape of possible theories of quantum gravity, and to understand whether it is necessary to include complicated degrees of freedom - such as those coming from string theory - in order to obtain a consistent theory of quantum gravity. This setup also provides a calculable framework for the study of black hole quantum mechanics. For example, the counting of black hole microstates is related to intersection theory on the moduli space of Riemann surfaces.