Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série MATH-IHES
Domaines hep-th
Date Lundi 16 Octobre 2017
Heure 14:30
Institut IHES
Salle Amphithéâtre Léon Motchane
Nom de l'orateur Schlenker
Prenom de l'orateur Jean-Marc
Addresse email de l'orateur
Institution de l'orateur Université du Luxembourg
Titre The renormalized volume of quasifuchsian manifolds
Résumé Quasifuchsian manifolds are an important class of hyperbolic 3-manifolds, classically parametrized by two copies of Teichmüller space. Their volume is infinite, but they have a well-defined finite "renormalized volume" which has nice properties, both analytic and "coarse". In particular, considered as a function over Teichmüller space, the renormalized volume provides a Kähler potential for the Weil-Petersson metric; moreover, it is within bounded additive constants of the volume of the convex core and is bounded from above by the Weil-Petersson distance between the conformal structures at infinity. After describing these properties, we will outline some recent applications (by Kojima, McShane, Brock, Bromberg, Bridgeman, and others) to the Weil-Petersson geometry of Teichmüller space or the geometry of hyperbolic 3-manifolds that fiber over the circle. We will then explain how properties of the renormalized volume suggest new questions and viewpoints on quasifuchsian manifolds. The talk will be accessible to nonexperts.
Numéro de preprint arXiv
Commentaires Séminaire Géométrie et groupes discrets
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