Random matrix models are ubiquitous in physics and have been

studied from many perspectives. One important application is

producing exactly solvable toy models of quantum gravity and

string theory. These models relate to deep mathematical

structures of the moduli space of Riemann surfaces. Recent

work has extended these models to open strings and surfaces

with boundaries. This generalization is less straightforward

that one imagines and involves the introduction of additional

degrees of freedom. These models have become relevant in

recent studies of the gravitational dual of the SYK model, two-dimensional black holes, and gravity with constant curvature.

Based on work done in collaboration with Edward Witten.