Séminaire - Mars
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: mars.pdf.
- 09/03/2022 - Simon Barazer (Université Paris-Saclay) - salle 421
Titre:
Surgeries on orientable metric ribbon graphs and recursion formula for the volumes of the moduli spaces.
Resumé:Metric
ribbon graphs are combinatorial toy models for surfaces with
boundaries, they are usefull tools in geometry that could be used to
compute the masur veech volumes for instance. Oriented metric ribbon
graphs (OMRG) are related to abelian differentials and bipartite maps.
The volumes of the moduli spaces of four-valent OMRG with fixed
boundary lenghts are piece-wise polynomials. It's possible to study
curves on an OMRG, I will introce a particular class of multi-curves
which I call admissibles and I will use them to perform surgeries on
the graph. On an OMRG it's possible to extract each vertex by surgeries
along a canonical admissible multi-curve. From this result I will show
that the volumes satisfy a recursion that correspond to excising a
"directed pant's" and is very similar to topological recursion. If it's
possible i will speak about the relation with topological recursion,
Hurwitz numbers and other structures in some particular cases.