Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Domaines hep-th
Date Jeudi 17 Mars 2022
Heure 11:00
Institut LPTHE
Salle bibliothèque du LPTHE, tour 13-14, 4eme étage
Nom de l'orateur Garcia-Failde
Prenom de l'orateur Elba
Addresse email de l'orateur
Institution de l'orateur IMJ-PRG
Titre Topological recursion and quantisation of spectral curves
Résumé For some decades, deep connections have been forming among enumerative geometry, complex geometry, intersection theory and integrability. The topological recursion is a universal procedure that helps building these connections that was introduced around 2007 by Chekhov, Eynard and Orantin. It associates to some initial data called spectral curve, consisting of a Riemann surface and some extra data, a doubly indexed family of differentials on the curve, which often encode some enumerative geometric information, such as volumes of moduli spaces, matrix model correlation functions and intersection numbers. After an introduction to topological recursion and its relation to different topics, I will focus on the integrability part. The quantum curve conjecture claims that one can associate to a spectral curve a differential equation, whose solution can be reconstructed by the topological recursion applied to the original spectral curve. I will present this problem in some simple cases and comment on some of the technicalities that arise when proving the conjecture for algebraic spectral curves of arbitrary rank, like having to consider non-perturbative corrections. The last part will be based on joint work with B. Eynard, N. Orantin and O. Marchal.
Numéro de preprint arXiv
Fichiers attachés
  • Darboux_EGF.pdf (1332458 bytes) OPEN

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