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 …

We prove that if Γ is an icc irreducible lattice in a product of connected non-compact rank
one simple Lie groups with finite center, then the II 1 factor L⁢(Γ) is prime. In particular, we …

We show that for a countable exact group, having positive first ℓ 2-Betti number implies
proper proximality in this sense of [3]. This is achieved by showing a cocycle superrigidity …

In this paper we introduce a new family of icc groups Γ Γ which satisfy the following product
rigidity phenomenon, discovered in Drimbe et al.(J Reine Angew Math, 2016. arXiv …

II1 FACTORS WITH EXOTIC CENTRAL SEQUENCE ALGEBRAS Page 1 J. Inst. Math.
Jussieu (2021) 20(5), 1671–1696 doi:10.1017/S1474748019000653 c Cambridge …

We introduce the notion of biexactness for general von Neumann algebras, naturally
extending the notion from group theory. We show that biexactness implies solidity for von …

Using Popa's deformation/rigidity theory, we investigate prime decompositions of von
Neumann algebras of the form L (R) for countable probability measure preserving …

In the first part of the paper, we survey several results from Popa's deformation/rigidity theory
on the classification of tensor product decompositions of large natural classes of II1 factors …

We generalize W∗-superrigidity results about Bernoulli actions of rigid groups to general
mixing Gaussian actions. We thus obtain the following: If Γ is any ICC group which is w-rigid …

We prove that any II 1 factor arising from a free ergodic probability measure preserving
action Γ↷ X of a product Γ= Γ 1×…× Γ n of icc hyperbolic, free product or wreath product …