We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral
invariants of sequences of locally symmetric spaces. Our main results are uniform versions …

Consider Sym (n) endowed with the normalized Hamming metric dn. A finitely generated
group Γ is P-stable if every almost homomorphism ρ nk: Γ→ Sym (nk)(ie, for every g, h∈ Γ …

We show that stationary characters on irreducible lattices Γ< G Γ<G of higher-rank
connected semisimple Lie groups are conjugation invariant, that is, they are genuine …

We show that the space of traces of free products of the form C (X 1)⁎ C (X 2), where X 1
and X 2 are compact metrizable spaces without isolated points, is a Poulsen simplex, ie …

Homology and homotopy complexity in negative curvature Page 1 DOI 10.4171/JEMS/971 J.
Eur. Math. Soc. 22, 2537–2571 c European Mathematical Society 2020 Uri Bader · Tsachik …

We study compact three-manifolds with boundary obtained by randomly gluing together
truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the …

A generalization of the double commutator lemma for normal subgroups is shown for
invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As …

We prove the following extension of Tits' simplicity theorem. Let kk be an infinite field, G an
algebraic group defined and quasi-simple over k, k, and G (k) G (k) the group of k k-rational …

We establish vanishing results for limits of characters in various discrete groups, most
notably irreducible lattices in higher rank semisimple Lie groups. This is achieved by …

We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It
follows that L is permutation stable, providing an example of an infinitely presented such …