A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to
have the unique trace property if its reduced C*-algebra has a unique tracial state. A …

In recent years scholars from a variety of branches of mathematics have made several
significant developments in the theory of group actions. Groups of Circle Diffeomorphisms …

This book offers to study locally compact groups from the point of view of appropriate metrics
that can be defined on them, in other words to study" Infinite groups as geometric objects" …

We present geometric conditions on a metric space (Y, dY) ensuring that, almost surely, any
isometric action on Y by Gromov's expander-based random group has a common fixed …

Stationary C -dynamical systems Page 1 © 2022 European Mathematical Society Published
by EMS Press and licensed under a CC BY 4.0 license J. Eur. Math. Soc. 25, 1783–1821 (2023) …

We study lattices in non‐positively curved metric spaces. Borel density is established in that
setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided …

A breakthrough result of B\'ar\'any, Hochman and Rapaport published in 2019 established
that every self-affine measure on $\mathbb {R}^ 2$ satisfying certain mild non-degeneracy …

The exponential growth rate of non-polynomially growing subgroups of GLrf is conjectured
to admit a uniform lower bound. This is known for non-amenable subgroups, while for …

We introduce a novel notion of local spectral gap for general, possibly infinite, measure
preserving actions. We establish local spectral gap for the left translation action …

We introduce the notion of joint spectrum of a compact set of matrices S⊂ GL d (C), which is
a multi‐dimensional generalization of the joint spectral radius. We begin with a thorough …