Related papers: Around the Hossz\'u-Gluskin theorem for $n$-ary gr…

Let N be the set of non-negative integer numbers, T the circle group and c the cardinality of the continuum. Given an abelian group G of size at most 2^c and a countable family F of infinite subsets of G, we construct "Baire many"…

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…

In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.

We prove Schlichting's theorem for approximate subgroups: if $\mathcal{X}$ is a uniform family of commensurable approximate subgroups in some ambient group, then there exists an invariant approximate subgroup commensurable with…

In analogy with epsilon-biased sets over Z_2^n, we construct explicit epsilon-biased sets over nonabelian finite groups G. That is, we find sets S subset G such that | Exp_{x in S} rho(x)| <= epsilon for any nontrivial irreducible…

We consider generalized metric spaces taking distances in an arbitrary ordered commutative monoid, and investigate when a class $\mathcal{K}$ of finite generalized metric spaces satisfies the Hrushovski extension property: for any…

We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary…

Krasnosselsky's art gallery theorem gives a combinatorial characterization of star-shaped sets in Euclidean spaces, similar to Helly's characterization of finite families of convex sets with non-empty intersection. We study colorful and…

This article takes the inspiration from two milestones in the study of non minimal actions of groups on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves and Ghys' freeness result in analytic regularity. Our…

This paper gathers four lectures, based on a mini-course at IMA in 2014, whose aim was to discuss the structure of approximate subgroups of an arbitrary group, following the works of Hrushovski and of Green, Tao and the author. Along the…

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…

We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…

In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of epsilon-quasi tilings for these groups. In this context, constructions of Ornstein and Weiss are extended by…

We study quasiminimal classes, i.e. abstract elementary classes (AECs) that arise from a quasiminimal pregeometry structure. For these classes, we develop an independence notion, and in particular, a theory of independence in $\M^{eq}$. We…

We generalise the definition of a group algebra so that it makes sense for non-locally compact topological groups, in particular, we require that the representation theory of the group algebra is isomorphic (in the sense of Gelfand-Raikov)…

We extend several techniques and theorems from geometric group theory so that they apply to geometric actions on arbitrary proper metric ARs (absolute retracts). A second way that we generalize earlier results is by eliminating freeness…

We generalize one part of Thurston's hyperbolic Dehn filling theorem to arbitrary-rank semisimple Lie groups by showing that certain deformations of extended geometrically finite subgroups of a semisimple Lie group are still extended…

We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces…

Following the continuing interest in the Urysohn space and, more specifically, the recent problem area of finding and comparing group structures on the Urysohn space we prove that there exists a non-abelian group structure on the Urysohn…

We generalize Hrushovski's Group Configuration Theorem to quasiminimal classes. As an application, we present Zariski-like structures, a generalization of Zariski geometries, and show that a group can be found there if the pregeometry…