Black hole entropy and the problem of universality

A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an embarrassment of riches: many different approaches to quantum gravity yield the same entropy, despite counting very different states. This "universality" suggests that some underlying feature of the classical theory may control the quantum density of states. I discuss the possibility that this feature is an approximate two-dimensional conformal symmetry near the horizon.