Speaker: Taisuke Hoshino (the University of Tokyo)

Title: Rigidity for graph-wreath product II₁ factors

Time/Date: June 9 (Tue), 2026, 4:45-6:15pm

Room: 126 Math. Sci. Building (It will be also online. The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)

Abstract: Given a graph C=(V, E) and a family of vertex groups (G_v) indexed by the set of vertices V, their graph product group G_C is the free product of (G_v), subject to the condition that elements from adjacent vertex groups commute. Then, the graph-wreath product group, a variant of graph product construction, is defined to be the semidirect product of a certain Bernoulli-type action on a graph product group. The rigidity problem for these constructions concerns how much information of the original graph or vertex groups remains in the group von Neumann algebras of their graph product or graph-wreath product groups. In this talk, we will review the recent progress on this topic and introduce our rigidity type results for graph-wreath product groups. We make use of the notion of bi-exactness by Ozawa for the proof.