Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  hepth 
Date  Jeudi 17 Mars 2022 
Heure  11:00 
Institut  LPTHE 
Salle  bibliothèque du LPTHE, tour 1314, 4eme étage 
Nom de l'orateur  GarciaFailde 
Prenom de l'orateur  Elba 
Addresse email de l'orateur  
Institution de l'orateur  IMJPRG 
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 nonperturbative corrections. The last part will be based on joint work with B. Eynard, N. Orantin and O. Marchal. 
Numéro de preprint arXiv  
Commentaires  
Fichiers attachés 
Pour obtenir l' affiche de ce séminaire : [ Postscript  PDF ]

[ English version ] 