The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

We consider amalgamated free product II1 factors M= M 1* BM 2* B… and use
“deformation/rigidity” and “intertwining” techniques to prove that any relatively rigid von …

We present some recent rigidity results for von Neumann algebras (II1 factors) and
equivalence relations arising from measure preserving actions of groups on probability …

In this article we study cocycles of discrete countable groups with values in ℓ 2 G and the
ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with …

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 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) …

We present a general setting to investigate 𝒰fin-cocycle superrigidity for Gaussian actions in
terms of closable derivations on von Neumann algebras. In this setting we give new proofs …

The author obtains some classification result for the map** class groups of compact
orientable surfaces in terms of measure equivalence. In particular, the map** class groups …

We show that the map** class group of a compact orientable surface with higher
complexity satisfies the following rigidity in the sense of measure equivalence: If the …

We study graph products of groups from the viewpoint of measured group theory. We first
establish a full measure equivalence classification of graph products of countably infinite …