The local community usually has a large heritage; and this a case for the implementation of the ISO 50001 standard. This is due to the fact that the Local Measurement System, recommended by the ISO 50001 standard [1], is not adapted and is not very efficient to identify the Energy Saving Fields Scope (ESFS) in the framework of communities whose ass...
One can observe that Coxeter groups and right-angled Artin groups share the same solution to the word problem. On the other hand, in his study of reflection subgroups of Coxeter groups Dyer introduces a family of groups, which we call Dyer groups, which contains both, Coxeter groups and right-angled Artin groups. We show that all Dyer groups have t...
We interpret the Hilbert entropy of a convex projective structure on a closed surface of higher genus as the Hausdorff dimension of the nondifferentiability points of the limit set in the full flag space F(R^3). Generalizations of this for hyperconvex representations are also discussed. An ingredient for the proofs is the concept of hyperplane coni...
We construct the first examples of infinite sharply 2-transitive groups which are finitely generated. Moreover, we construct such a group that has Kazhdan property (T), is simple, has exactly four conjugacy classes, and we show that this number is as small as possible.
Dans cette note d'exposition, nous revenons sur la classification des actions exceptionnelles de PSL_2 (Z/pZ) sur un ensemble à p éléments, annoncée par Galois dans sa dernière lettre à Chevalier.
We present a simple tool to perform analysis with groups such as SL(n,R) and SL(n,Z), that has been introduced by Vincent Lafforgue in his study of non-unitary representations, in connection with the Baum-Connes conjecture and strong property (T). It has been later applied in various contexts: operator algebras, Fourier analysis, geometry of Banach...
The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and quantum synchronous strategies for non-local games. We observe in particular that simple spectral gap estimates...
We consider semi-continuity of certain dimensions on group schemes.
Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.
