Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebras

Sven Raum (Stockholm University)

09-Aug-2021, 06:30-07:30 (3 years ago)

Abstract: n the 90's, Nebbia conjectured that a group of tree automorphisms acting transitively on the tree's boundary must be of type I, that is, its unitary representations can in principal be classified. For key examples, such as Burger-Mozes groups, this conjecture is verified. Aiming for a better understanding of Nebbia's conjecture and a better understanding of representation theory of groups acting on trees, it is natural to ask whether there is a characterisation of type I groups acting on trees. In 2016, we introduced in collaboration with Cyril Houdayer a refinement of Nebbia's conjecture to a trichotomy, opposing type I groups with groups whose von Neumann algebra is non-amenable. For large classes of groups, including Burger-Mozes groups, we could verify this trichotomy. In this talk, I will motivate and introduce the conjecture trichotomy for groups acting on tress and explain how von Neumann algebraic techniques enter the picture.

group theory

Audience: researchers in the discipline


Symmetry in Newcastle

Organizer: Michal Ferov*
*contact for this listing

Export talk to