Weil–Petersson geometry and the BGW KdV tau function

It was conjectured by Witten and proven by Kontsevich that a generating function for intersection numbers on the moduli space of curves is a tau function of the KdV hierarchy, now known as the Kontsevich–Witten tau function.  Mirzakhani reproved this theorem via the study of Weil–Petersson volumes of moduli spaces of hyperbolic surfaces.  In this lecture I will describe another collection of intersection numbers on the moduli space of curves whose generating function is a tau function of the KdV hierarchy, known as the Brezin–Gross–Witten tau function.  The proof uses Weil–Petersson geometry and an analogue of Mirzakhani's argument.