AMENABILITY

Schedule

• 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.