Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série WORK-CONF
Domaines math
Date Jeudi 17 Août 2017
Heure 11:00
Institut LPTENS
Salle Room Conf. IV
Nom de l'orateur Saito
Prenom de l'orateur Masa-Hiko
Addresse email de l'orateur
Institution de l'orateur University of Kobe
Titre Moduli spaces of connections and Higgs bundles over curves and Geometric Theory of equations of Painlevé type.
Résumé Geometric theory of equations of Painlevé type are based on moduli spaces of stable parabolic connections on a family of smooth projective curves of arbitrary genus. We will start with algebraic constructions of moduli spaces of parabolic connections and singular parabolic Higgs bundles on a smooth projective curve. Riemann-Hilbert correspondence from a family of moduli spaces of singular connections to the corresponding moduli spaces of (generalized) monodromy data induces the isomonodromic differential equations. An analysis of RH correspondence shows the geometric Painlevé property of isomonodromic differential equations associated to each type of singular connections. Next, I will investigate explicit geometric structures of moduli spaces of parabolic connections and Higgs bundles. On a Zariski dense open set of each moduli space one can define a canonical coordinate system associated to apparent singularities and their duals. The spectral curves for Higgs bundles play essential roles for this explicit geometry. If time permits, we will explain more geometric structures of moduli spaces.
Numéro de preprint arXiv
Commentaires Workshop on "Exceptional and ubiquitous Painlevé equations for Physics". Please see webpage https://indico.in2p3.fr/event/14720/
Fichiers attachés

Pour obtenir l' affiche de ce séminaire : [ Postscript | PDF ]

[ Annonces ]    [ Abonnements ]    [ Archive ]    [ Aide ]    [ ]
[ English version ]