Group Actions and Rigidity: Around the Zimmer Program, Paris

15 avr. 2024, 08:30 → 5 juil. 2024, 20:30 Europe/Paris

Amphitheater Hermite / Darboux (IHP)

Thematic trimester programme with short courses, seminars and workshops

April 15 to July 5, 2024 at the Institut Henri Poincaré, Paris

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Presentation of the trimester

This term focuses on rigidity of group actions with some focus on issues that arise out of Zimmer's groundbreaking work in the 1980's. Areas of interest range from local and global rigidity of group actions to special rigidity phenomena in small dimensions to symmetry groups of geometric structures to measure rigidity results for quite general group actions with hyperbolicity.

 

This broad area has seen a very large number of dramatic breakthroughs in recent years. The goal of the term is to bring together experts and people in adjacent areas to share ideas and techniques and to foster additional breakthroughs. There will also be a significant component of the term dedicated to introducing younger participants to the broad area.

Introductory School:

April 15 to 19, 2024: Rigidity, Dynamics and Geometric Structures, held at CIRM, Marseille

Workshops: 

April 29 to Saturday, May 4, 2024: Low Dimensional Actions (IHP, Paris)

May 27 to 31, 2024: Group Actions with Hyperbolicity and Measure Rigidity (IHP, Paris)

June 10 to 14, 2024: Actions of Large Groups, Geometric Structures, and the Zimmer Program (IHP, Paris)

Mini-courses:

Mini-courses will be held in amphitheater Darboux in IHP. The standard format will be three 2h long lectures during one week for each mini-course. 

Titles and abstracts of mini-courses: click here.

• Bertrand Deroin (Université de Cergy & CNRS): Week of May 6
• Thang Nguyen (Florida State University): Week of May 13
• Romain Dujardin (Sorbonne Université): Week of May 20
• Cyril Houdayer (ENS Paris): Week of June 3
• Tim de Laat (University of Münster): Week of June 3
• Karin Melnick (University of Luxembourg): Week of June 17
• Kurt Vinhage (University of Utah): Week of June 17

Weekly seminar

In weeks not containing workshops there will be a research seminar on Mondays and Wednesdays at 3pm. Webpage of the seminar: link

Organising committe:

• Aaron Brown (Northwestern University)
• David Fisher (Rice University)
• Kathryn Mann (Cornell University)
• Vincent Pecastaing (Université Côte d’Azur)
• Ralf Spatzier (University of Michigan)

Scientific committe:

• Serge Cantat (Université de Rennes I)
• Alex Eskin (University of Chicago)
• Étienne Ghys (ENS Lyon)
• Federico Rodriguez Hertz (Pennsylvania State University)
• Amie Wilkinson (University of Chicago)

 

Back to the thematic trimester main page 

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Programme coordinated by the Centre Emile Borel at IHP

 

Sorbonne Université, CNRS

Poster T2 2024 GAR.pdf

mercredi 24 avril

15:00 Finite Fourier transform by Yves Benoist

Abstract: On a cyclic group of prime order, the non-principal Dirichlet characters together with their Fourier transforms are functions that vanish at 0 and whose modulus is constant outside 0. Do there exist other functions with these properties? I will explain the history of this question and give a positive answer for non-safe primes. The proof relies on Floer homology.

lundi 29 avril

1 Registration/ Welcome coffee

2 Opening Speech by the Deputy Director of IHP, Prof Domonique Mouhanna

3 Workshop 'Low dimensional actions' - April 29 to May 4 - 1st day

mardi 30 avril

4 Workshop 'Low dimensional actions' - April 29 to May 4 - 2nd day

18:00 Cocktail dinner party

mercredi 1 mai

09:00 Public holiday

jeudi 2 mai

5 Workshop 'Low dimensional actions' - April 29 to May 4 - 3rd day

vendredi 3 mai

6 Workshop 'Low dimensional actions' - April 29 to May 4 - 4th day

samedi 4 mai

7 Workshop 'Low dimensional actions' - April 29 to May 4 - 5th day

lundi 6 mai

10:00 Orderability of lattices in semi-simple Lie groups. Mini course by Bertrand Deroin, Université de Cergy & CNRS

Abstract : There are several interesting ways of ordering groups, but we will focus here on the notion of left-orderability, namely the existence of a total ordering on the group invariant by left translations. In the lectures, we will provide the complete classification of left-orders on irreducible lattices in a semi-simple Lie group of real rank at least 2, based on work of Deroin and Hurtado: such orders exist only if the Lie group has a
-factor and are obtained by pull-back. This answers positively conjectures of Ghys and Witte in the beginning of the 90's. Techniques for the proof include 1) random walks on the group of homeomorphism of the real line, 2) group of almost-periodic homeomorphism of the real line 3) Furstenberg's Poisson formula, 4) dynamics of Cartan subgroups. If time permit, we will discuss the situation in the rank one case.

15:00 Seminar by Colin Guillarmou, Université Paris-Saclay

mardi 7 mai

10:00 Orderability of lattices in semi-simple Lie groups. Mini course-2 by Bertrand Deroin

14:00 Orderability of lattices in semi-simple Lie groups. Mini course-3 by Bertrand Deroin

lundi 13 mai

10:00 Local rigidity of higher rank lattice actions on flag manifolds. Mini course by Thang Nguyen, Florida State University

Abstract: The main focus of the minicourse is to study local rigidity of standard actions of uniform lattices in higher rank Lie groups on flag manifolds within the space of actions by homeomorphisms. The rigidity in more differentiable actions often relies on the stability of uniform hyperbolic systems. In the setting of actions by homeomorphisms, We explore a much weaker form of stability derived from coarse geometry. We will go over how dynamics and coarse geometry intertwine to achieve a desired local rigidity. At the end of the minicourse, we will extend our discussion to other natural boundary actions.
The outlined of topics in the minicourse include:
Local rigidity: problems and results.
Stability of uniform hyperbolic systems and uniformly transverse foliations.
Geometry and coarse geometry of symmetric spaces.
Weyl chamber flows.
Suspension and developing.
Barycenter and its regularity.
Proof of local rigidity for actions on flag manifolds.
Actions on geodesic boundaries and some related actions.

14:00 Seminar by Barbara Schapira, Université de Rennes

mardi 14 mai

10:00 Local rigidity of higher rank lattice actions on flag manifolds. Mini course-2 by Thang Nguyen

mercredi 15 mai

10:00 Local rigidity of higher rank lattice actions on flag manifolds. Mini course-3 by Thang Nguyen

15:00 Seminar by Bruno Duchesne, Université Paris Saclay

mercredi 22 mai

15:00 Seminar by Thibault Lefeuvre, Sorbonne Université