Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série MATH-IHES
Domaines hep-th
Date Lundi 18 Juin 2018
Heure 16:30
Institut IHES
Salle Centre de conférences Marilyn et James Simons
Nom de l'orateur Loustau
Prenom de l'orateur Brice
Addresse email de l'orateur
Institution de l'orateur Rutgers University
Titre Bi-Lagrangian structures and Teichmüller theory
Résumé A bi-Lagrangian structure on a manifold is the data of a symplectic form and a pair of transverse Lagrangian foliations. Equivalently, it can be defined as a para-Kähler structure, i.e. the para-complex analog of a Kähler structure. After discussing interesting features of bi-Lagrangian structures in the real and complex settings, I will show that the complexification of any Kähler manifold has a natural complex bi-Lagrangian structure. I will then specialize this discussion to moduli spaces of geometric structures on surfaces, which typically have a rich symplectic geometry. We will see that that some of the recognized geometric features of these moduli spaces are formal consequences of the general theory while revealing new other features, and derive a few well-known results of Teichmüller theory. Time permitting, I will present the construction of an almost hyper-Kähler structure in the complexification of any Kähler manifold. This is joint work with Andy Sanders.
Numéro de preprint arXiv
Commentaires Séminaire "Géométrie et groupes discrets"
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