Coboundary expansion (with F 2 coefficients), and variations on it, have been the focus of
intensive research in the last two decades. It was used to study random complexes, property …

Expander graphs have been, during the last five decades, the subject of a most fruitful
interaction between pure mathematics and computer science, with influence and …

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a
common form: can all groups be approximated by asymptotic homomorphisms into the …

This paper is motivated by recent developments in group stability, high dimensional
expansion, local testability of error correcting codes and topological property testing. In Part …

In recent years, there has been a considerable amount of interest in the stability of a finitely-
generated group Γ with respect to a sequence of groups {G n} n= 1∞, equipped with bi …

Abstract We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups
from several angles. We give a short, elementary proof that finitely generated nilpotent …

A discrete countable group G is matricially stable if the finite dimensional approximate
unitary representations of G are perturbable to genuine representations in the point-norm …

We define the notion of self-tracial stability for tracial von Neumann algebras and show that
a tracial von Neumann algebra satisfying the Connes embedding problem (CEP) is self …

We study the notion of permutation stability (or P-stability) for countable groups. Our main
result provides a wide class of non-amenable product groups which are not P-stable. This …

We prove that every uniform approximate homomorphism from a discrete amenable group
into a symmetric group is uniformly close to a homomorphism into a slightly larger symmetric …