Resurgence and large genus asymptotics of intersection numbers

• Alessandro Giacchetto (ETH Zurich)

In this talk, I will present a new approach to the computation of the large genus asymptotics of Witten–Kontsevich intersection numbers. Our technique is based on a resurgent analysis of the n-point function of such intersection numbers, which are computed via determinantal formulae, and relies heavily on the presence of an underlying first order differential system. With this approach, we are able to extend the recent results of Aggarwal with the computation of subleading corrections, and to obtain completely new results on r-spin and Theta-class intersection numbers. Based on the joint work with B. Eynard, E. Garcia-Failde, P. Gregori, D. Lewański.

Counting with random walks

• Baptiste Louf (CNRS - Université de Bordeaux)

We are interested in counting combinatorial maps by genus and size, asymptotically as both the size and the genus go to infinity. The original motivation is to use these counting estimates to study the geometry of random maps in large genus and their hyperbolic behaviour. While enumeration in one parameter is a very well studied topic with many powerful tools available, this problem is a case of bivariate enumeration, is a rather new topic with very few results known at the moment. Our method consists in studying a recurrence formula for these maps and modeling it by a random walk, forgetting completely about the combinatorics of the model.