Mercredi 23 mars 2016
IRMA
This one-day workshop on Teichmüller theory will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on March 23th, 2016.
Organizers : K. Ohshika (Osaka) and A. Papadopoulos (Strasbourg)
The speakers will include :
- V. Alberge (Strasbourg)
- S. Lelièvre (Orsay)
- G. Mondello (Rome)
- J.-M. Schlenker (Luxembourg)
The speakers will present recent results on Teichmüller space and its boundary at infinity. Vincent Alberge will defend his PhD thesis. Graduate students, young and senior researchers are all welcome.
For information and registration, please contact the organizers : K. Ohshika or A. Papadopoulos
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Mercredi 23 mars 2016
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09:30
Jean-Marc Schlenker, Université du Luxembourg
The renormalized volume of quasifuchsian manifolds and extremal length
Abstract.--- Quasifuchsian hyperbolic manifolds have infinite volume, but they have a well-defined "renormalized" volume, closely related to the Liouville functional. It has interesting "analytic" properties, in particular it provides a Kähler potential for the Weil-Petersson metric of the boundary at infinity, but also interesting "coarse". We will describe an analogy between the renormalized volume and the volume of the convex core, where the length of laminations on the boundary of the convex core is analoguous to the extremal length of measured foliations at infinity. -
10:30
Pause -
11:00
Gabriele Mondello, Università ``Sapienza'' di Roma
On the Dolbeault cohomological dimension of the moduli space of Riemann surfaces
Abstratc.-- Abstract The moduli space M_g of Riemann surfaces of genus g is (up to a finite étale cover) a complex manifold and so it makes sense to speak of its Dolbeault cohomological dimension, i.e. the highest k such that H^{0,k}(M_g,E) does not vanish for some holomorphic vector bundle E on M_g. The conjecturally optimal bound is g-2, which is verified for g=2,3,4,5. I can prove that such dimension is at most 2g-2. The key point is to show that the Dolbeault cohomological dimension of each stratum of translation surfaces is at most g (still non-optimal bound). In order to do that, I produce an exhaustion function, whose complex Hessian has controlled index: in the construction of such a function basic geometric properties of translation surfaces come into play. -
14:00
Samuel Lelièvre, Université Paris-Sud
Flat surfaces and arithmetic of algebraic integers.
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15:00
Vincent Alberge, Université de Strasbourg
Extremal length and the geometry of Teichmüller space (PhD defense)