Erwin Schrödinger Institute, Vienna


Special semester, February - July 2007



The Erwin Schrödinger 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),
Vadim A. Kaimanovich (Bremen, Germany) ,
Klaus Schmidt (Vienna, Austria)

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:

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

Amenability beyond groups 

February 26 - March 17, 2007

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

This workshop is partially supported by the Marie Curie Conferences and Training Courses Programme MSCF-CT-2006-045987 GROUPS.  

In addition to talks on current research the programme of this workshop will contain several minicourses (4-6 lectures each) as well as some shorter lecture series which will provide a comprehensive introduction to various aspects of amenability and report on recent advances in the area. These courses should be accessible to mathematicians at all levels (starting from advanced Ph.D. students).

The following minicourses are planned:

Alekos Kechris (Caltech): Extreme amenability: Some new interactions between combinatorics, logic and topological dynamics,  June 18-20, 2007

Abstract: This minicourse will provide an introduction to the property of extreme amenability (or fixed point on compacta property) of topological groups, which arises in the context of topological dynamics and is related to asymptotic geometric analysis, especially concentration of measure phenomena, and describe its connections with ideas from finite combinatorics, particularly Ramsey theory, and logic.

Schedule of lectures for the week June 18 - 22, 2007

Nicolas Monod (Geneva): Some topics on amenable actions,  June 25 - 29, 2007

In this series of lectures, we shall study some aspects of the classical question of the existence of invariant means on a set under a group action. We shall restrict ourselves to the "naked" setting where no topology or measure-theory is involved.  We shall on the one hand address classical results, giving for instance a short proof of Tarski's theorem on paradoxical decompositions.  On the other hand, we present a few new aspects that have been historically overlooked, regarding e.g. amenable actions of non-amenable groups.  We will also present a few problems that are simple to formulate but appear to be unsolved. 

Schedule of lectures for the week June 25 - 29, 2007

Dave Witte Morris (Lethbridge): Some discrete groups that cannot act on 1-dimensional manifolds,  July 2 - 6, 2007

We will see that it is easy to give an algebraic characterization of the amenable groups that have a nontrivial action on the real line. The course will then discuss relations between amenability, the Furstenberg boundary, and actions of lattices on 1-dimensional manifolds (or other spaces). Many questions remain open.

Schedule of lectures for the week July 2 - 6, 2007

Volodymir Nekrashevych (Texas A&M): Contracting self-similar groups,  July 9 - 13, 2007

Contracting self-similar groups appear naturally as iterated monodromy groups of expanding  self-coverings of orbispaces. They include many examples of non-elementary amenable groups. An open question is if they all are amenable. We will discuss relation of contracting groups to dynamical systems and their properties related to amenability (growth, absence of free subgroups, amenability of the associated groupoids of germs, etc.).

Schedule of lectures for the week July 9 - 13, 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

Back to table of contents.


Participation is free. In order to register for participation in one of the workshops, please send an email to 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. 

Back to table of contents.

Last modified on May 2, 2007