Volumes and Random Matrices

This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The article is based on a lecture at the conference on the Mathematics of Gauge Theory and String Theory, University of Auckland, January 2020. It has been submitted to a special issue of the Quarterly Journal of Mathematics in memory of Michael Atiyah.)