Group Actions and Rigidity: Around the Zimmer Program
Workshop: Actions of Large Groups, Geometric Structures, and the Zimmer Program
June 10 to 14, 2024 - IHP, Paris
Analyzing actions of semisimple Lie groups and their lattices has been a main stay of rigidity in dynamics and geometry, and has been studied since Zimmer’s call to action in the 1980s. It ties together ergodic theory and smooth dynamics, geometry and Lie theory, via geometric structures, coarse geometry, order structures, measure and cocycle rigidity amongst others. In turn it has motivated major problems in those areas.
The workshop will emphasize advances and connections between smooth dynamics and the Zimmer program over the last decade, such as the work on hyperbolic actions of higher rank abelian groups. It brought about major advances, especially breakthroughs in the Zimmer conjecture about actions in low dimensions, the classification of lattice actions on tori and nilmanifolds in the presence of Anosov elements, and recently on arbitrary manifolds, on conformal Lorentz structures as well as local rigidity results for actions of lattices on boundaries. Crucially it will feature new tools developed.
Many exciting problems remain, especially assuming invariant dynamical or geometric structures for the action, or equivalently studying such structures with lots of symmetry.
Speakers:
- Danijela Damjanovic (KTH)
- Tim De Laat (University of Münster)
- Bassam Fayad (University of Maryland)
- Charles Frances (University of Strasbourg)
- Cyril Houdayer (ENS Paris)
- Mitul Islam (MPI Leipzig)
- Homin Lee (Northwestern University)
- Karin Melnick (University of Luxembourg)
- Vincent Pecastaing (Université Côte d'Azur)
- Federico Rodriguez-Hertz (PennState University)
- Victoria Sadovskaya (PennState University)
- Sven Sandfeldt (KTH)
- Alp Uzman (University of Utah)
- Wouter Van Limbeek (University of Illinois Chicago)
- Kurt Vinhage (University of Utah)
- Zhenqi Wang (Michigan State University)
- Amanda Wilkens (University of Texas)
- Abdelghani Zeghib (ENS Lyon)
Organsing committe:
- Aaron Brown (Northwestern University)
- David Fisher (Rice University)
- Karin Melnick (University of Luxembourg)
- Vincent Pecastaing (Université Côte d'Azur)
