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 …

This article presents a proof of the Feldman-Moore theorem on Cartan subalgebras in W*-
algebras based on the non-commutative Stone equivalence between Boolean inverse …

Kolmogorov–Sinai entropy is an invariant of measure-preserving actions of the group of
integers that is central to classification theory. There are two recently developed invariants …

We prove that for any free ergodic probability measure-preserving action F n↷(X, μ) of a free
group on n generators F n, 2≤ n≤∞, the associated group measure space II1 factor …

We prove that for any free ergodic probability measure preserving action Γ→(X, μ) of a non-
elementary hyperbolic group, or a lattice in a rank one simple Lie group, the associated …

We introduce the notion of proper proximality for finite von Neumann algebras, which
naturally extends the notion of proper proximality for groups. Apart from the group von …

R.–Ozawa a montré dans [21] que, pour un groupe cci hyperbolique, le facteur de type II1
associé est solide. En devéloppant une nouvelle approche, qui combine les méthodes de …

We prove that for any group G in a fairly large class of generalized wreath product groups,
the associated von Neumann algebra LG completely" remembers" the group G. More …

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 prove a “unique crossed product decomposition” result for group measure space II 1
factors L∞(X)⋊ Γ arising from arbitrary free ergodic probability measure preserving (pmp) …