Measured and Geometric Group Theory, Rigidity, Operator Algebras
Théorie mesurée et géométrique des groupes, rigidité, algèbres d’opérateurs
HYBRID RESEARCH SCHOOL / 5 – 9 October 2020
HYBRID RESEARCH SCHOOL SCHEDULE
(Marseille, France local time)
Measure versus topological dynamics have witnessed dramatic progress in the last ten years, and fascinating parallels have be drawn between these two theories. For instance the notion of full group became central in both settings. Similarly, the collection of stabilizers for non free actions led to the emerging topic of invariant random subgroups (IRS) and their topological counterparts : uniform recurrent subgroups (URS).
Geometric group theory and measured group theory consist in a kind of « sociological » study of groups via Gromov’s notions of topological couplings, resp. measure equivalence, and is intimately related with topological, resp. measured, dynamics of groups. Recently, a notion has been intensely studied that interpolates between measured and topological dynamics : Lp-measure equivalence.
Rigidity phenomena are omnipresent both in measure and geometric group theory in particular when dealing with higher rank lattices. Since the fundamental work of Margulis, an impressive amount of work has been devo- ted to generalize and strengthen it. Recently, various Von Neumann versions of Margulis’ theorem that had been suggested by Connes have been proved. In spite of these impressive progresses, many natural problems remain wide open, for instance very little is known for irreducible lattices in product of rank 1 simple Lie groups. Lastly, full groups have proved to produce rigid situations in terms of IRS and URS. Meanwhile, along the last years various phenomena of dizzying flexibility have been discovered especially among IRS.
The goal of this fall school is to immerse young researchers in these beau- tiful and quickly evolving subjects through 4 mini-courses completed by 6 additional one-hour talks. Special slots will be dedicated to exercise sessions.
Discussion rooms will be available to registered participants via the link above. Your access code to the rooms is provided by the organizers.
This page is accessible with a password issued by CIRM.
Rémi Boutonnet (Université de Bordeaux) Character rigidity and non-commutative ergodic theory
Mikael de la Salle (CNRS ENS Lyon) Group actions on Lp spaces : dependence on p