Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series MATH-IHES
Subjects hep-th
Date Monday 16 October 2017
Time 14:30
Institute IHES
Seminar Room Amphithéâtre Léon Motchane
Speaker's Last Name Schlenker
Speaker's First Name Jean-Marc
Speaker's Email Address
Speaker's Institution Université du Luxembourg
Title The renormalized volume of quasifuchsian manifolds
Abstract 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.
arXiv Preprint Number
Comments Séminaire Géométrie et groupes discrets

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