Status  Confirmed 
Seminar Series  MATHIHES 
Subjects  hepth 
Date  Monday 16 October 2017 
Time  14:30 
Institute  IHES 
Seminar Room  Amphithéâtre Léon Motchane 
Speaker's Last Name  Schlenker 
Speaker's First Name  JeanMarc 
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 3manifolds, classically parametrized by two copies of Teichmüller space. Their volume is infinite, but they have a welldefined 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 WeilPetersson metric; moreover, it is within bounded additive constants of the volume of the convex core and is bounded from above by the WeilPetersson 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 WeilPetersson geometry of Teichmüller space or the geometry of hyperbolic 3manifolds 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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