  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.)
