Abstracts for Geometric recursion learning seminar

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.

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.

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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 $\overline{\mathcal{M}}_{g',n'}$).

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.