Franco-Swiss nanoconference

Tuesday 18 December 2012

EPFL, room CO 121


(click titles for abstracts)

  • 9:15–10:15  Yair Glasner
    Actions of linear groups on sets and on probability spaces

    Let A = Z! be the full symmetric group of a countable set and B = Aut(X,µ) the automorphism group of a standard probability space. I will discuss the role of the Zariski topology in the study of representation of countable linear groups into these two Polish groups. I will illustrate the method by discussing the following two theorems.

    Theorem 1 (joint with Dennis Gulko). For every sharply 2-transitive linear permutation group Γ, there exists a near field N (i.e. a skew field which is distributive only from the left) such that Γ is the semidirect product of N* and N.

    Theorem 2. If a countable linear group acts by measure preserving transformations on a probability space (X,µ) in such a way that almost every point has an amenable stabilizer. Then the stabilizers are all contained in a common amenable normal subgroup.

  • Coffee break

  • 10:45–11:45  Kate Juschenko
    On simple amenable groups

    We will discuss amenability of the topological full group of a minimal Cantor system. Together with the results of H. Matui this provides examples of finitely generated simple amenable groups. Joint with N. Monod.

  • Lunch break

  • 14:15–15:15  Tatiana Nagnibeda
    On percolation characterization of non-amenability

    We will discuss Benjamini–Schramm non-amenabitily conjecture in relation with two values measuring non-amenability of a Cayley graph — the spectral radius of the random walk and the isoperimetric constant.

  • Coffee break

  • 15:45–16:45  Narutaka Ozawa
    Quantum correlations and Kirchberg's conjecture

    I will talk about Tsirelson's problem on quantum correlations of independent bipartite systems. The problem is known to be equivalent to Kirchberg's and Connes's conjectures, and hence has a close connection with Gromov's problem asking whether every group is sofic.

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