Related papers: Hyperlinear approximations to amenable groups come…
We establish a close link between the amenability of a unitary representation $\pi$ of a group $G$ (in the sense of Bekka) and the concentration property (in the sense of V. Milman) of the corresponding dynamical system $(\s_\pi,G)$, where…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…
We provide sharp stability estimates for the Alexandrov Soap Bubble Theorem in the hyperbolic space. The closeness to a single sphere is quantified in terms of the dimension, the measure of the hypersurface and the radius of the touching…
We generalize the classical definition of effectively closed subshift to finitely generated groups. We study classical stability properties of this class and then extend this notion by allowing the usage of an oracle to the word problem of…
We prove that if a proper metric space is quasi-isometric to a finitely generated group and to a space with a horoball over a finitely generated group, then that space is quasi-isometric to a rank-one symmetric space or the real line.
Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are…
We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq \mathrm{SL}(n,…
In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said…
We introduce the notion of a ``sofic $\mathcal{C}$-action'' of one group on another by automorphisms, for $\mathcal{C}$ a class of groups. We show that if $\mathcal{C}$ is the class of (i) sofic, (ii) hyperlinear, (iii) linear sofic or (iv)…
We develop a theory of soficity for actions on graphs and obtain new applications to the study of sofic groups. We establish various examples, stability and permanence properties of sofic actions on graphs, in particular soficity is…
We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action…
We study amenability of definable and topological groups. Among our main technical tools is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and some results around measures. As an application we…
We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability…
We say that two free probability-measure-preserving actions of countable groups are Shannon orbit equivalent if there is an orbit equivalence between them whose associated cocycle partitions have finite Shannon entropy. We show that if the…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
A sofic group $G$ is said to be flexibly stable if every sofic approximation to $G$ can converted to a sequence of disjoint unions of Schreier graphs by modifying an asymptotically vanishing proportion of edges. We establish that if…
In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…