Erwin Schrödinger Institute, Vienna

Amenability

Special semester, February - July 2007

Contents:
Introduction  
Workshops
Registration

Introduction

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. Day 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.;

There will be two separate main periods of activity in the first (end of February - April) and in the second (May - July) parts of the semester. During the first period there was a three-week workshop

The second period of the programme will last from May 1 to July 31. During this time there will be a workshop

Algebraic, geometric and probabilistic aspects of amenability

June 18 - July 14, 2007

The ESI will offer a number of Junior Fellowships to support the participation of young researchers in the programme. Support for junior researchers consists of a daily allowance of 70 Euros per day (which is sufficient to cover the accommodation in Vienna with the special ESI rate; ESI does not provide travel support). Senior participants will be supported at the rate of 80 Euros per day.

Applications for participation and financial support should be sent to the organizers at  aesi@esi.ac.at.

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Registration

Participation is free. In order to register for participation in one of the workshops, please send an email to aesi@esi.ac.at. The ESI secretaries will provide you with the practical information concerning accommodation etc. in due time.
If you want to give a talk, please give us a (tentative) title, although we can not guarantee that  all the talks will be included in the  final programme. 

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