- September 26 and 27, 2013, at UMPA, ENS Lyon.
François le Maître,
- 10h-10h50: Sven Raum
- 11h-11h50: Rémi Boutonnet
- 14h-14h50: François le Maître
- 15h-15h50: Benben Liao
- 16h30-17h20: François Lemeux
Abstracts of the talks
- 10h-10h50: Hiroshi Ando
- 11h-11h50: Jean Roydor
Hiroshi Ando: « Ultraproducts, QWEP von Neumann algebras, and the Effros-Maréchal topology ».
Haagerup and Winsløw studied the space of von Neumann algebras acting on a separable Hilbert space equipped with so-called
Effros-Maréchal topology. They proved that this topology is closely linked to the modular theory, tracial ultraproducts and Kirchberg's QWEP conjecture. They in particular showed that a separable type II1 factor is Rω-embeddable if and only if it is the Effros-Maréchal limit of matrix algebras. In this talk we study further connection among ultraproducts, QWEP and Effros-Maréchal topology. The key ingredients are structural results about non-tracial ultraproducts of von Neumann algebras established last year by the speaker and Haagerup. (Joint work with Uffe Haagerup and Carl Winsløw).
Rémi Boutonnet: « On Maximal amenable subalgebras in hyperbolic group von Neumann algebras ».
We showed recently with A. Carderi that any maximal amenable subgroup in a hyperbolic group gives rise to a maximal amenable subalgebra in the associated group von Neumann algebra.
I will present a proof of this result and discuss some related open questions.
François Lemeux: « Fusion rules, and applications, for free wreath products by the quantum permutation group ».
After giving a few notions and examples of compact quantum groups, I will recall some results of Banica on fusion rules binding irreducible representations of free quantum groups. Then, I will describe the fusion rules of free wreath products of discrete (classical) groups by the quantum permutation group, quantum analogues of classical wreath products by the permutation group and then discuss some applications as approximation properties.
Benben Liao: « Strong Banach property (T) and its applications ».
In this talk, I will talk about strong Banach property (T) introduced by Vincent Lafforgue. I will also present consequences that expanders constructed by finite quotients of a discrete group with strong Banach property (T) does not admit a uniform imbedding in any Banach space of type >1, and that any isometric action of a locally compact group with strong Banach property (T) in a Banach space of type >1 has a fixed point. Any higher rank simple algebraic groups over a non archimedean local field and its co-compact lattices have strong Banach property (T). Finally, I will talk about some arguments used in the proof of this theorem.
François le Maître: « Topological generators for full groups ».
If two pmp equivalence relations are orbit equivalent, then their full groups are conjugated, so that full groups provide an invariant of orbit equivalence as topological groups. This motivates their study on their own. Here we will focus on the topological rank of the full group, that is, the minimal number of elements needed to generate a dense subgroup. We will also discuss « genericity phenomenons » for topological generators, motivated by the Schreier-Ulam theorem which states that the generic pair in a compact metrisable connected group does generate a dense subgroup.
Sven Raum: « Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity ».
Baumslag-Solitar groups form a class of basic examples in combinatorial group theory. They exhibit interesting features of rigidity and flexibility at the same time. It is an open problem to classify non-amenable Baumslag-Solitar groups up to Gromov's measure equivalence. In 2011 Kida proved that for a big class of non-amenable Baumslag-Solitar groups every measure equivalence coupling which is aperiodic on the natural commensurable subgroups implies isomorphism of the respective Baumslag-Solitar groups. In this work we generalise Kida's result to all non-amenable Baumslag-Solitar groups. At the same time, our proof is new and simpler. It is based on a totally disconnected group associated with any aperiodic inclusion of probability measure preserving equivalence relations, which allows us to recover the relative profinite completion of Baumslag-Solitar groups in our setting.
Jean Roydor: « A noncommutative Amir-Cambern type theorem ».
We will present the following result: let A be a separable nuclear C*-algebra or a von Neumann algebra, if the Banach-Mazur cb-distance between A and an arbitrary C*-algebra B is small enough, then A and B
are *-isomorphic. As an intermediate result, we compare the Kadison-Kastler distance and the Banach-Mazur cb-distance.