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La première journée commune Luxembourg-Lorraine-Strasbourg "Géométrie en action, actions en géométrie" aura lieu à Strasbourg le 3 février 2017.

  • Vendredi 3 février 2017

  • 11:00

    Daniel Monclair, Université de Luxembourg

    Critical exponent and Hausdorff dimension in Anti de Sitter geometry

    Given a convex cocompact group of isometries of the hyperbolic space, its critical exponent (a number measuring the growth of orbits) is equal to the Hausdorff dimension of its limit set. This equality provides a link between the asymptotic behavior of the dynamics on the hyperbolic space and the local geometry of the boundary. When the limit set is a topological circle, this number is at least 1. A theorem of Bowen states that this lower bound can only be reached if the limit set is a geometric circle.
    We will see that this relationship between asymptotic dynamics and local geometry of the boundary also exists for groups acting on Anti de Sitter space (the Lorentzian analogue of hyperbolic space). We will also discuss a Lorentzian version of Bowen's Theorem.
    This is a joint work with O. Glorieux (University of Luxembourg).
  • 14:00

    Jérémy Blanc, Université de Bâle

    Topological simplicity of the Cremona groups

    I will talk about the group of birational maps of the n-th dimensional space over a field k, which can also be algebraically described as the group of automorphisms of the free extension of k over n indeterminates. This group, called Cremona group of rank n, will be showed to be simple, endowed with topology, over any infinite field. Two elements are moreover always connected by an affine line, so the group is path-connected.
    Joint work with Susanna Zimmermann (Toulouse).