Alternatively have a look at the program.

## Presentation of the seminar on Geometric recursion - POSTPONED to Oct. 26 --

## Presentation of the seminar on Geometric recursion

## The Definition of the Geometric Recursion

Given some initial data the Geometric Recursion is a procedure that gives mapping class group invariants.

We will define the Geometric Recursion and give a proof that this in fact well defined.

## Good definition of GR and the case of continuous functions on Teichmüller spaces

## Topological recursion and enumerative problems

In this talk, we introduce the notion of topological recursion. Moreover, we relate it to several enumerative problems, such as generalized Catalan numbers and variants of Hurwitz numbers.

## Lifting Topological Recursion to Geometric Recursion

In previous talks, Geometric Recursion (GR) was introduced, as well as the principle of Topological Recursion (TR), for which some examples were furnished. Both procedures allow to produce, from initial data, an infinite family of "invariants". The question we tackle here is the relation between those families of invariants and between the initial data. The aim of this talk is to show that, starting from TR with a certain class of spectral curves, one can reproduce the same invariants by GR.

## Geometric recursion for Masur-Veech volumes?

The Masur-Veech volume $b_{g,n}$ of $\overline{\mathcal{M}}_{g,n}$ can be defined in two ways. Firstly, as the integral over $\overline{\mathcal{M}}_{g,n}$ of a certain analytic function $B_{g,n}$. Secondly as the coefficient of the leading term of some enumerative problem (here a certain type of quadrangulations in genus $g$). There is a formula for the Masur-Veech volume $b_{g,n}$ as a polynomial of integrals of psi-classes (on various $\overline{\mathcal{M}}_{g',n'}$).

## Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials

We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained by intersection numbers on the strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel-Veech constants for all strata.

## Topological recursion and intersection theory 1

In this first talk, we discuss generalities about intersection theory on the moduli space of stable curves, with particular emphasis on computational tools like Kontsevich model for psi intersections, Mirzakhani's recursion and Mumford formula for lambda classes.

## Topological recursion and intersection theory 2

In this second talk, we investigate the connection between topological recursion (TR) and intersection theory on the moduli space of stable curves. In particular, we will show how to compute TR amplitudes associated to a spectral curve in terms of intersections of psi classes and a certain class built from the spectral curve itself. Examples will include Kontsevich and Mirzakhani's recursion and ELSV formula.

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