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French-Japanese workshop on Teichmüller spaces and surface mapping class groups


Du 4 au 5 juin 2015

IRMA
Programme

The French-Japanese workshop en Teichmüller spaces and surface mapping class groups will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on June 4-5, 2015.

Organizers : A. Papadopoulos and V. Alberge (Strasbourg)

The invited speakers include :

  • N. A’Campo (Basel)
  • J. Aramayona (Toulouse)
  • V. Disarlo (Bloomington)
  • L. Ji (Ann Arbor)
  • N. Kawazumi (Tokyo)
  • Y. Kuno (Tokyo)
  • H. Miyachi (Osaka)
  • K. Ohshika (Osaka)
  • T. Sakasai (Tokyo)
  • A. Sambarino (Orsay)
  • J.-M. Schlenker (Luxembourg)
  • S. Yamada (Tokyo)

The talks will be in English and they are intended for a general audience. Graduate students and young mathematicians are welcome.

Registration is required (and free of charge) at this link. Hotel booking can be asked for through the registration link.

For practical matters and other questions please contact the organizers :

  • Jeudi 4 juin 2015

  • 09:00

    Norbert A'campo, Basel

    A real analytic cell complex for braid groups

  • 10:00

    Coffee break
  • 10:20

    Andrés Sambarino, Université Paris 6

    A Riemannian metric on (certain open subsets of) character varieties of hyperbolic groups, invariant under outer automorphisms

  • 11:20

    Yusuke Kuno, Tsuda College

    A homology valued invariant for trivalent fatgraph spines

  • 12:30

    Lunch At The Maison Universitaire France-Japon (jsps Offices In Strasbourg)

    Everybody is invited. We shall all leave together at 12:20.

  • 14:30

    Nariya Kawazumi, The University of Tokyo

    A tensorial description of the Turaev cobracket on genus 0 compact surfaces

    We give a complete tensorial description of the Turaev cobracket on genus 0 compact surfaces with respect to the standard group-like expansion. There the Bernoulli numbers appear twice: one appearance comes from the tensorial description of the homotopy intersection form given by Massuyeau and Turaev, and the other from a geometric lemma given by Fukuhara, Kuno and the speaker. The result seems to suggest some relation between the Turaev cobracket and the Kashiwara-Vergne problem in the formulation by Alekseev and Torossian.
  • 15:30

    Coffee break
  • 16:00

    Hideki Miyachi, Osaka University

    Toward the complex geometry of Teichmüller space from extremal length geometry - The Levi form of extremal length functions

  • 17:00

    Jean-Marc Schlenker, Université du Luxembourg

    The renormalized volume of quasifuchsian manifolds

  • 19:30

    Dinner Offered To All Participants

    At the restaurant "Le Petit Bois vert" (2 quai de la Bruche, Petite France quarter)

  • Vendredi 5 juin 2015

  • 09:00

    Sumio Yamada, Gakushuin University

    Metric geometry on the positive orthant

  • 10:00

    Coffee break
  • 10:30

    Lizhen Ji, University of Michigan

    Compactification and fundamental domains for geometrically finite groups

  • 11:30

    Javier Aramayona, Université de Toulouse

    Finite rigidity for curve complexes

    A celebrated theorem of Ivanov, extended by Korkmaz and Luo, states that the curve complex C(S) of a surface is "simplicially rigid": every automorphism of C(S) is, except in a few well-understood cases, induced by an element of the mapping class group Mod(S). In this talk we will give a construction, for every surface S, of a finite subcomplex X(S) of C(S) that is also "rigid", in the sense that every injection of X(S) into C(S) is the restriction of an element of Mod(S). These finite rigid sets enjoy some curious properties; for instance, in the case of S a sphere with punctures, X(S) happens to coincide with the generator for the homology of C(S) identified by Birman-Broaddus-Menasco. We will then explain how to express C(S) as an increasing union of finite rigid sets, thus offering a new proof of the theorem of Ivanov-Korkmaz-Luo. Time permitting, we will describe an alternate proof of this latter result, due to Jesus Hernandez, which has interesting consequences to the rigidity of self-maps of C(S).
  • 14:00

    Valentina Disarlo, Indiana University

    On the geometry of the flip graph

    The flip graph of an orientable punctured surface is the graph whose vertices are the ideal triangulations of the surface (up to isotopy) and whose edges correspond to flips. Its combinatorics is crucial in works of Thurston and Penner's decorated Teichmuller theory. In this talk we will explore some geometric properties of this graph, in particular we will see that it provides a coarse model of the mapping class group in which the mapping class groups of some subsurfaces are strongly convex. We will also establish some bounds on the growth of the diameter of the ip graph modulo the mapping class group, extending a result of Sleator-Tarjan-Thurston. This is a joint work with Hugo Parlier.
  • 15:00

    Coffee break
  • 15:30

    Takuya Sakasai, The University of Tokyo

    On homology cobordisms of surfaces of genus 1

  • 16:30

    Ken'ichi Ohshika, Osaka University

    Geography of closed 3-manifolds within character varieties