The Brownian Map

Nina Holden won the 2021 Maryam Mirzakhani New Frontiers Prize for her work on random surfaces and the mathematics of quantum gravity. I’d like to tell you what she did… but I’m so far behind I’ll just explain a bit of the background.

Suppose you randomly choose a triangulation of the sphere with n triangles. This is a purely combinatorial thing, but you can think of it as a metric space if each of the triangles is equilateral with all sides of length 1.

This is a distorted picture of what...