## Probabilistic Operator Algebra Seminar: Tensor decompositions of II$_1$ factors arising from extensions of amalgamated free product groups

Seminar | September 18 | 3:45-5:45 p.m. | 748 Evans Hall

Rolando de Santiago, UC Presidential Postdoctoral Fellow, UCLA

Department of Mathematics

We describe a family of groups whose von Neumann algebras satisfy the following rigidity phenomenon: all tensor decompositions of $L(\Gamma )$ into II$_1$ factors necessarily arise from direct product decompositions of the group Γ. This class includes many iterated amalgamated free product groups such as right-angled Artin groups, Burger-Mozes groups, Higman group, integral two-dimensional Cremona groups. As a consequence, we obtain several new examples of groups that give rise to prime factors.

dvv@math.berkeley.edu