Wreath-like Product Groups and Their von Neumann Algebras: W*-superrigidity and Outer Automorphism Groups

Explore a lecture by Professor Adrian Ioana from the University of California, San Diego, delivered at the BIMSA-Tsinghua Quantum Symmetry Seminar, focusing on wreath-like product groups and their von Neumann algebras. Learn about these new class of groups that are related to classical wreath products but with distinct properties, including many that possess Kazhdan's property (T). Discover two major rigidity results for von Neumann algebras of wreath-like product groups: first, how certain ICC groups with property (T) are W*-superrigid, confirming Connes' rigidity conjecture from the 1980s; and second, how isomorphisms between their group von Neumann algebras stem from group isomorphisms. Understand the groundbreaking application that any countable group can be realized as the outer automorphism group of L(G) for an ICC property (T) group G, providing the first calculations of outer automorphism groups of II1 factors from property (T) groups and serving as a converse to Connes' 1980 result.