Operator Theory Seminar – Professor Ionut Chifan, PhD | Physics and Astronomy | The University of Iowa – Iowa Now

ProfessorIonut Chifan; University of Iowa

Abstract: In this talk I will introduce a new class of groups, which we call textit{wreath-like products}. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have strong fixed point properties including Kazhdan's property (T). In this paper, we establish several new rigidity results for von Neumann algebras of wreath-like products. In particular, we obtain the first continuum of property (T) groups whose von Neumann algebras satisfy Connes' rigidity conjecture and the first examples of W$^*$-superrigid groups with property (T). We also compute automorphism groups of von Neumann algebras of a wide class of wreath-like products; as an application, we show that for every finitely presented group $Q$, there exists a property (T) group $G$ such that $Out(L(G))cong Q$. This is based on new joint work with Adrian Ioana, Denis Osin and Bin Sun.

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Operator Theory Seminar - Professor Ionut Chifan, PhD | Physics and Astronomy | The University of Iowa - Iowa Now