collaborators

11 papers

math.DS2026

Superrigidity for representations of transverse measured groupoids

Filippo Sarti, Alessio Savini

For , let be a connected, simply connected, semisimple algebraic group over some local field of characteristic zero. Let $G_i=\mathbf{G}_i(κ_i)…

math.OA2025

Uniformly bounded representations of discrete measured groupoid into finite Von Neumann algebras

Alessio Savini

Let be a -discrete ergodic groupoid. Consider a finite Von Neumann algebra with separable predual. We prove that every uniformly bounded measura…

math.GR2025

Some explicit cocycles on the Furstenberg boundary for products of isometries of hyperbolic spaces and

Michelle Bucher, Alessio Savini

Nicolas Monod showed that the evaluation map between the measurable cohomology of the action of a connected semisimple Lie gr…

math.GR2025

Continuous cochains on Furstenberg boundaries and injectivity of the comparison map

Michelle Bucher, Alessio Savini

Monod proved that any continuous cohomology of a semisimple Lie group can be represented by a measurable cocycle on the associated Furstenberg boundary, which we upgraded to an…

math.DS2025

Measurable bounded cohomology of measured groupoids

Filippo Sarti, Alessio Savini

We introduce the notion of measurable bounded cohomology for measured groupoids, extending continuous bounded cohomology of locally compact groups. We show that the measurable boun…

math.DS2025

Boundaries and equivariant maps for ergodic groupoids

Filippo Sarti, Alessio Savini

We give a notion of boundary pair for measured groupoids which generalizes the one introduced by Bader and Furman \cite{BF14} for locally compact gr…