Ionuţ Chifan - University of Iowa We show that any infinite collection (Γn)n∈N of icc, hyperbolic, property (T) groups satisfies the following von Neumann algebraic \emph{infinite product rigidity} phenomenon. If Λ is an arbitrary group such that L(⊕n∈N\Gn)≅L(Λ) then there exists an infinite direct sum decomposition Λ=(⊕n∈NΛn)⊕A with A icc amenable such that, for all n∈N, up to amplifications, we have L(Γn)≅L(Λn) and L(⊕k≥nΓk)≅L((⊕k≥nΛk)⊕A). The result is sharp and complements the previous finite product rigidity property found in \cite{CdSS16}. Using this we provide an uncountable family of restricted wreath products \G=Σ≀Δ of icc, property (T) groups Σ, Δ whose wreath product structure is recognizable, up to a normal amenable subgroup, from their von Neumann algebras L(Γ). Along the way we highlight several applications of these results to the study of rigidity in the C∗-algebra setting. This is based on a joint work with Bogdan Udrea.