Abstract: 

Black holes have long been known to possess an entropy proportional to their horizon area, and an important goal in quantum gravity is to characterize the microstates responsible for this entropy.  One way to approach this task is to identify symmetries of the black hole under which the microstates are expected to transform.  In this talk, I will describe how a set of conformal symmetries can be identified for generic axisymmetric Killing horizons, and further show how these symmetries lead to the black hole entropy via a Cardy formula.  I will also discuss symmetries that appear for more generic subregions, and construct an associated set of charges.  In this case, the area of the bounding surface and a collection of curvature invariants appear as Casimirs of the resulting symmetry algebra, providing an interesting class of observables that can be associated to subregions in general relativity.