The Erwin Schrodinger Institute (ESI) will host a special semester devoted to AMENABILITY during the period end of February 2007 - mid-July 2007.

The organizers are:

Anna Erschler (Orsay, France) anna.erschler@math.u-psud.fr,

Vadim A. Kaimanovich (Bremen, Germany) v.kaimanovich@iu-bremen.de,

Klaus Schmidt (Vienna, Austria) klaus.schmidt@univie.ac.at

The notion of amenability is a natural generalization of finiteness or compactness. It was introduced in 1929 by J. von Neumann (following the work of Hausdorff, Banach and Tarski; in 1955 M. M. Dye first called it amenability). Amenable groups are those which admit an invariant mean (rather than an invariant probability measure, which is the case for finite or compact groups). This classical notion has been generalized in many directions and currently plays an important role in various areas, such as dynamical systems, von Neumann and C*-algebras, operator K-theory, geometric group theory, random walks, etc.

The semester will be centered around several interconnected research subjects at the crossroads of Analysis, Algebra, Geometry, Dynamics and Probability. More specifically, we are going to discuss the following topics:

○ groups of intermediate growth, non-elementary amenable groups;

○ self-similar groups and iterated monodromy groups of rational maps;

○ graphed equivalence relations and amenability; L2 cohomology;

○ amenable groupoids; topological amenability of boundary actions;

○ amenability at infinity; Baum--Connes and Novikov conjectures;

○ amenability and rigidity; bounded cohomology;

○ amenable algebras;

○ quasi-isometric classification of amenable groups, geometricity of various group properties;

○ Dixmier's conjecture on characterization of amenability in terms of unitarizable representations;

○ generalizations of amenability: A-T-menabilty (Haagerup property); groups without free subgroups; superamenability;

○ random walks and other probabilistic models on amenable groups;

○ quantitative invariants of amenable groups: growth, isoperimetry, asymptotic entropy, etc.;