Group Theory, Measure, and Asymptotic Invariants

Abstract

The workshop ‘Group Theory, Measure, and Asymptotic Invariants’ organized by Miklos Abert (Budapest), Damien Gaboriau (Lyon) and Andreas Thom (Leipzig) was held 18 - 24 August 2013. The event was a continuation of the previous Oberwolfach workshop ‘Actions and Invariants of Residually Finite Groups: Asymptotic Methods’ organized by Miklos Abert (Budapest), Damien Gaboriau (Lyon) and Fritz Grunewald (Dusseldorf) that was held September 5 - September 11, 2010. Fritz Grunewald passed away in March 2010 and Andreas Thom joined the organizing team.

The workshop aimed to study finitely generated groups and group actions using ergodic and measure theoretic methods, incorporating asymptotic invariants, such as ${\ell }^2$-invariants, the rank gradient, cost, torsion growth, entropy-type invariants and invariants coming from random walks and percolation theory.

The participant body came from a wide range of areas: finite and infinite group theory, geometry, ergodic theory, graph theory, topology, probability theory, representation theory, von Neumann algebras and ${\ell }^2$-theory. The participants typically did not speak each other’s mathematical dialect fluently. To address this situation, the organizers asked the speakers to put a special emphasis on the first, introductory part of their talks. This aspect worked very well.

As a general rule, the organizers asked speakers to talk about specific subjects, not just any nice piece of their research. In some cases, this meant sacrificing hearing about some new results from excellent mathematicians that were further away from the workshop’s main directions.