AMR-RMA

(after joint works with V. Delecroix, E. Goujard and P. Zograf)

We will start with a count of metric integer ribbon graphs (after Kontsevich and Norbury). The answer is expressed in terms of Witten-Kontsevich correlators, which will be introduced in the talk (and which should not scare the audience in advance). Having counted ribbon graphs, we will count square-tiled surfaces. In this way we will secretly count Masur-Veech volume of the moduli space of quadratic differentials, but this would, mostly remain as a secret. We will move to Mirzakhani’s count of simple closed geodesics on hyperbolic surfaces. At first glance, it might seem unrelated to the previous count. We will see, however, that the two counts are equivalent. We will proceed with a description of random geodesic multicurves and of random square-tiled surfaces in large genus. We will conclude with a universal asymptotic formula for the Witten-Kontsevich correlators predicted by Delecroix, Goujard, Zograf and myself and recently proved by Amol Aggarwal. I will do my best to make the talk self-contained and accessible to everybody.