Ergodic theory in its broadest sense is the study of group actions on measure spaces.
Historically the discipline has tended to concentrate on the framework of integer actions, in …

The core material of the book should be accessible to third year students, requiring only a
basic acquaintance with group theory, metric spaces, and point-set topology. I tried to keep …

We provide new examples of acylindrically hyperbolic groups arising from actions on
simplicial trees. In particular, we consider amalgamated products and HNN-extensions, one …

This article combines the features of a survey and a research paper. It presents a review of
some results obtained during the last decade in problems related to the dynamics of branch …

arXiv:1009.0132v1 [math.GR] 1 Sep 2010 Page 1 arXiv:1009.0132v1 [math.GR] 1 Sep 2010
Orbit Equivalence and Measured Group Theory Damien Gaboriau∗ May, 2010 Abstract We …

We survey some of the progress made recently in the classification of von Neumann
algebras arising from countable groups and their measure preserving actions on probability …

We give a survey of recent classification results for von Neumann algebras arising from
measure preserving group actions on probability spaces. This includes II 1 factors with …

We consider group measure space II $ _ {1} $ factors $ M= L^{\infty}(X)\rtimes\Gamma $
arising from Bernoulli actions of ICC property (T) groups $\Gamma $(more generally, of …

We provide a gentle introduction, aimed at non-experts, to Borel combinatorics that studies
definable graphs on topological spaces. This is an emerging field on the borderline between …

Consider a free ergodic measure-preserving profinite action Γ↷ X (ie, an inverse limit of
actions Γ↷ X n, with X n finite) of a countable property (T) group Γ (more generally, of a …