Statut  Confirmé 
Série  IPHTPHM 
Domaines  mathph 
Date  Jeudi 21 Décembre 2017 
Heure  11:00 
Institut  IPHT 
Salle  Salle Claude Itzykson, Bât. 774 
Nom de l'orateur  Gaëtan Borot 
Prenom de l'orateur  
Addresse email de l'orateur  
Institution de l'orateur  Max Plank Bonn 
Titre  Geometric recursion 
Résumé  I will present a new formalism, which takes as input a functor $E$ from a category of surfaces with their mapping classes as morphisms, to a category of topological vector spaces, together with glueing operations, as well as a small amount of initial data, and produces as output functorial assignments $S \mapsto \Omega_S$ in $E(S)$. This construction is done by summing over all excisions of homotopy class of pair of pants decompositions of $S$, and we call it ``geometric recursion''. The topological recursion of Eynard and Orantin appears as a projection of the geometric recursion when $E(S)$ is chosen to be the space of continuous functions over the Teichmuller space of $S$, valued in a Frobenius algebra  and the projection goes via integration over the moduli space. More generally, the geometric recursion aims at producing all kinds of mapping class group invariant quantities attached to surfaces. \\ \\ This is based on joint work with J.E. Andersen and N. Orantin. 
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