Group Actions with Hyperbolicity and Measure Rigidity

Amphithéâtre Hermite / Darboux (Institut Henri Poincaré)

Amphithéâtre Hermite / Darboux

Institut Henri Poincaré

11 rue Pierre et Marie Curie 75005 Paris

Group Actions and Rigidity: Around the Zimmer Program

Workshop: Group Actions with Hyperbolicity and Measure Rigidity 

May 27 to 31, 2024 - IHP, Paris

Actions with some degree of hyperbolicity arise naturally in many mathematical contexts. Many natural problems reduce ti the classification of invariant measures or closed invariant sets. For instance, given a manifold equipped with an action by a large (not virtually-cyclic, though not necessarily higher-rank) group, under certain dynamical, geometric, or algebraic criteria on the action, one might hope to classify (1) all stationary or invariant measures and (2) all orbit closures for the action. In a geometrically related setting, given a partially hyperbolic diffeomorphism, one might ask when a u-Gibbs measure is necessarily SRB or when an equivariant foliation is necessarily minimal.  

This workshop will bring together experts working in homogeneous dynamics, smooth hyperbolic dynamics, complex and arithmetic dynamics, and group actions to discuss new results and techniques related to the rigidity of invariant measures and orbit closures for hyperbolic group actions.

Confirmed speakers:

  • Timothée Bénard (University of Warwick)
  • Serge Cantat (Université de Rennes & CNRS)
  • Sylvain Crovisier (Université Paris-Saclay & CNRS)
  • Nicolas de Saxce (Université Sorbonne Paris-Nord & CNRS)
  • David Fisher (Rice University)
  • Seung uk Jang (Université de Rennes)
  • Asaf Katz (University of Michigan)
  • Victor Kleptsyn (CNRS & Université de Rennes)
  • Manuel Luthi (EPFL)
  • Hee Oh (Yale University)
  • Rafael Potrie (Universidad de la República)
  • Megan Roda (University of Chicago)
  • Roland Roeder (Indiana University)
  • Federico Rodriguez-Hertz (PennState University)
  • Bruno Santiago (Universidade Federal Fulminense)
  • Cagri Sert (University of Zürich)
  • Omri Solan (Hebrew University)
  • Rosemary Eliott Smith (University of Chicago)
  • Zhiyuan Zhang (CNRS & Université Paris-Nord)


Organising Committe:

  • Aaron Brown (Northwestern Universty)
  • Romain Dujardin (Sorbonne Université)
  • Simion Filip (University of Chicago)
  • David Fisher (Rice University)
  • Davi Obata (Brigham Young University)


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Conference GAR2024