## Dr. Vadim Alekseev

### Project leader

Technische Universität Dresden

E-mail: vadim.alekseev(at)tu-dresden.de

Telephone: +49 351 463-34065

## Publications within SPP2026

We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as comparison of its orbit, Koopman and groupoid-left-regular representations. Besides that, we unify several recent results about paradoxicality in semigroups and groupoids, relating embeddings of Thompson's group V into full groups of ample étale groupoids.

**Related project(s):****2**Asymptotic geometry of sofic groups and manifolds

We show a rigidity result for subfactors that are normalized by a representation of a lattice Γ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of *L*Γ which is normalized by the natural copy of Γ is trivial or of finite index.

**Related project(s):****2**Asymptotic geometry of sofic groups and manifolds

We provide a large class of discrete amenable groups for which the complex group ring has several C*-completions, thus providing partial evidence towards a positive answer to a question raised by Rostislav Grigorchuk, Magdalena Musat and Mikael Rørdam.

**Related project(s):****2**Asymptotic geometry of sofic groups and manifolds

We give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an invariant random subgroup and a character. We use von Neumann algebras to show that all invariant random positive definite functions on groups with infinite conjugacy classes which integrate to the regular character are constant.

**Related project(s):****2**Asymptotic geometry of sofic groups and manifolds