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 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 …

Cartan subalgebras in von Neumann algebras associated with graph product groups Page 1
Groups Geom. Dyn. 18 (2024), 749–759 DOI 10.4171/GGD/756 ฉ 2023 European Mathematical …

We prove rigidity properties for von Neumann algebraic graph products. We introduce the
notion of rigid graphs and define a class of II $ _1 $-factors named $\mathcal {C} _ {\rm …

In this paper we study various rigidity aspects of the von Neumann algebra LpΓq where Γ is
a graph product group [Gr90] whose underlying graph is a certain cycle of cliques and the …

Using computations in the bidual of B (L 2 M) we develop a new technique at the von
Neumann algebra level to upgrade relative proper proximality to full proper proximality. This …

For a simple graph Γ and for unital C*-algebras with GNS-faithful states (A v, φ v) for v∈ V Γ,
we consider the reduced graph product (A, φ)=⁎ v, Γ (A v, φ v), and show that if every C …

We introduce the extension graph of graph product of groups and study its geometry. This
enables us to study properties of graph products of groups by exploiting large scale …

In this paper we show that the cloning system construction of Skipper and Zaremsky [SZ21],
under sufficient conditions, gives rise to Thompson-Like groups which are stable; in …

The main topics of this thesis include: von Neumann algebras, Coxeter groups, graph
products, approximation properties, rigidity theory and commutator estimates. We discuss …