We prove that a type II1 factor M can have at most one Cartan subalgebra A satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class… (More)

We prove that if a countable discrete group Γ is w-rigid, i.e. it contains an infinite normal subgroup H with the relative property (T) (e.g. Γ = SL(2, Z) ⋉ Z, or Γ = H × H with H an infinite Kazhdan… (More)

We study group measure space II1 factors M = L∞(X, μ)⋊σ G where G are discrete ICC groups containing infinite normal subgroups with the relative property (T) and σ are “malleable” and “clustering”… (More)

We prove that if a countable group Γ contains a non-amenable subgroup with centralizer infinite and “weakly normal” in Γ (e.g. if Γ is non-amenable and has infinite center or is a product of infinite… (More)

We prove a classification result for properly outer actions σ of discrete amenable groups G on strongly amenable subfactors of type II, N ⊂ M , a class of subfactors that were shown to be completely… (More)

We give a new proof of a result of Ozawa showing that if a von Neumann subalgebra Q of a free group factor LFn, 2 ≤ n ≤ ∞ has relative commutant diffuse (i.e. without atoms), then Q is amenable.

For each 2 ≤ n ≤ ∞, we construct an uncountable family of free ergodic measure preserving actions αt of the free group Fn on the standard probability space (X,μ) such that any two are non orbit… (More)

For each group G having an infinite normal subgroup with the relative property (T) (e.g. G = H × K, with H infinite with property (T) and K arbitrary) and each countable abelian group Λ we construct… (More)

We prove several unique prime factorization results for tensor products of type II 1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups… (More)

We consider certain conditions for abstract lattices of commuting squares, that we prove are necessary and sufficient for them to arise as lattices of higher relative commutants of a subfactor. We… (More)