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.
