# Breuillard, Emmanuel 1977-

Overview
Works: 15 works in 23 publications in 2 languages and 209 library holdings Conference papers and proceedings Editor, Contributor, Opponent, Thesis advisor, Author
Publication Timeline
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Most widely held works by Emmanuel Breuillard
Thin groups and superstrong approximation by Thin Groups and Super-strong Approximation( Book )

3 editions published in 2014 in English and held by 136 WorldCat member libraries worldwide

"This is a collection of surveys and primarily expository articles focusing on recent developments concerning various quantitative aspects of 'thin groups.' There are discrete subgroups of semisimple Lie groups that are both big (Zariski dense) and small (of infinite covolume). This dual nature leads to many intricate questions. Over the past few years, many new ideas and techniques, arising in particular from arithmetic combinatorics, have been involved in the study of such groups, leading, for instance, to far-reaching generalizations of the strong approximation theorem in which congruence quotients are shown to exhibit a spectral gap, referred to a superstrong aproximation. This book provides a broad panorama of a very active field of mathematics at the boundary between geometry, dynamical systems, number theory, and combinatorics. It arose from the MSRI hot topics workshop of the same name in February 2012."
Rigidité, groupe fondamental et dynamique by Martine Babillot( Book )

1 edition published in 2002 in French and held by 37 WorldCat member libraries worldwide

Rigidité, groupe fondamental et dynamique by Martine Babillot( Book )

4 editions published in 2002 in French and held by 11 WorldCat member libraries worldwide

Simply-laced isomonodromy systems by Ph Boalch( Book )

2 editions published in 2012 in English and held by 7 WorldCat member libraries worldwide

On the hyperbolicity of general hypersurfaces by Damian Brotbek( Book )

2 editions published in 2017 in English and held by 6 WorldCat member libraries worldwide

Géométrie des groupes localement compacts. Arbres. Action ! by Adrien Le Boudec( )

1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide

In Chapter 1 we investigate the class of locally compact lacunary hyperbolic groups. We characterize locally compact groups having one asymptotic cone that is a real tree and whose natural isometric action is focal. We also study the structure of lacunary hyperbolic groups, and prove that in the unimodular case subgroups cannot satisfy a law. We apply the previous results in Chapter 2 to solve the problem of the existence of cut-points in asymptotic cones for connected Lie groups. In Chapter 3 we prove that Neretin's group is compactly presented and give an upper bound on its Dehn function. We also study metric properties of Neretin's group, and prove that some remarkable subgroups are quasi-isometrically embedded. In Chapter 4 we study a family of groups acting on a tree, and whose local action is prescribed by some permutation group. We prove among other things that these groups have property (PW), and exhibit some simple groups in this family. In Chapter 5 we introduce the relation range of a finitely generated group, which is the set of lengths of relations that are not generated by relations of smaller length. We establish a link between simple connectedness of asymptotic cones and the relation range of the group, and give a large class of groups having a relation range as large as possible
Marches aléatoires, equirépartition, et sous-groupes denses dans les groupes de Lie by Emmanuel Breuillard( Book )

2 editions published in 2003 in French and held by 2 WorldCat member libraries worldwide

This dissertation consists of two relatively independent parts. The first part, more probabilistic in nature, deals with random walks on Lie groups and especially with equidistribution properties of random walks after a very large time. Chapter 2 is devoted to the study of equidistribution of finitely supported symmetric walks on nilpotent Lie groups. In Chapter 3, we prove a local limit theorem for product of random matrices in the Heisenberg group and we obtain a probabilistic equivalent of Ratner's equidistribution theorem for unipotent random walks on homogeneous spaces. Chapter 4 is independent and entirely devoted to the local limit theorem on R^d with a study of the speed of convergence. The second part, of a more algebraic fiavor, deals with dense free subgroups of real and p-adic Lie groups. We show a topological version of Tits' alternative asserting that any subgroup of GL(n.k), where k is a local field, contains either a relatively open solvable subgroup, or a relatively dense free subgroup. We then provide several applications of this theorem to the theory of profinite groups, of amenable actions and of Riemannian foliations
Sous-groupes boréliens des groupes de Lie by Nicolas de Saxcé( )

1 edition published in 2012 in French and held by 1 WorldCat member library worldwide

Given a Lie group G, we investigate the possible Hausdorff dimensions for a measurable subgroup of G. If G is a connected nilpotent Lie group, we construct measurable subgroups of G having arbitrary Hausdorff dimension, whereas if G is compact semisimple, we show that a proper measurable subgroup of G cannot have Hausdorff dimension arbitrarily close to the dimension of G
Sommes, produits et projections des ensembles discrétisés by Weikun He( )

1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

Dans le cadre discrétisé, la taille d'un ensemble à l'échelle $delta$ est évaluée par son nombre de recouvrement par $delta$-boules (également connu sous le nom de l'entropie métrique). Dans cette thèse, nous étudions les propriétés combinatoires des ensembles discrétisés sous l'addition, la multiplication et les projections orthogonales. Il y a trois parties principales. Premièrement, nous démontrons un théorème somme-produit dans les algèbres de matrices, qui généralise un théorème somme-produit de Bourgain concernant l'anneau des réels. On améliore aussi des estimées somme-produit en dimension supérieure obtenues précédemment par Bougain et Gamburd. Deuxièmement, on étudie les projections orthogonales des sous-ensembles de l'espace euclidien et étend ainsi le théorème de projection discrétisé de Bourgain aux projections de rang supérieur. Enfin, dans un travail en commun avec Nicolas de Saxcé, nous démontrons un théorème produit dans les groupes de Lie parfaits. Ce dernier résultat généralise les travaux antérieurs de Bourgain-Gamburd et de Saxcé
Joint Spectrum and Large Deviation Principles for Random Products of Matrices by Cagri Sert( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

Après une introduction générale et la présentation d'un exemple explicite dans le chapitre 1, nous exposons certains outils et techniques généraux dans le chapitre 2.- dans le chapitre 3, nous démontrons l'existence d'un principe de grandes déviations (PGD) pour les composantes de Cartan le long des marches aléatoires sur les groupes linéaires semi -simples G. L'hypothèse principale porte sur le support S de la mesure de la probabilité en question et demande que S engendre un semi-groupe Zariski dense. - Dans le chapitre 4, nous introduisons un objet limite (une partie de la chambre de Weyl) que l'on associe à une partie bornée S de G et que nous appelons le spectre joint J(S) de S. Nous étudions ses propriétés et démontrons que J(S) est une partie convexe compacte d'intérieur non-vide dès que S engendre un semi -groupe Zariski dense. Nous relions le spectre joint avec la notion classique du rayon spectral joint et la fonction de taux du PGD pour les marches aléatoires. - Dans le chapitre 5, nous introduisons une fonction de comptage exponentiel pour un S fini dans G, nous étudions ses propriétés que nous relions avec J(S) et démontrons un théorème de croissance exponentielle dense. - Dans le chapitre 6, nous démontrons le PGD pour les composantes d'Iwasawa le long des marches aléatoires sur G. L'hypothèse principale demande l'absolue continuité de la mesure de probabilité par rapport à la mesure de Haar.- Dans le chapitre 7, nous développons des outils pour aborder une question de Breuillard sur la rigidité du rayon spectral d'une marche aléatoire sur le groupe libre. Nous y démontrons un résultat de rigidité géométrique
Benjamini-Schramm convergence of locally symmetric spaces by Mikołaj Frączyk( )

1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

Le sujet principal de ce mémoire est le comportement asymptotique de la géométrie et topologie des variétés localement symétriques Gamma\ X quand le volume tend vers l'infini. Notre premier résultat porte sur la convergence Benjamini-Schramm des 2 ou 3-variétés hyperboliques arithmétiques. Une suite d'espaces localement symétriques (Gamma_n\ X) converge Benjamini-Schramm vers l'espace symétrique X si pour chaque R>0 la limite de \Vol((\Gamma\X)_{<R})/Vol(\Gamma\bs X). On montre qu'il existe une constante réelle C=C_R satisfaisant la propriété suivante: pour chaque réseau arithmétique de congruence Gamma de \PGL(2,R) ou PGL(2,C) sans torsion on a Vol ((Gamma\ X)_{<R})<= C_R \ Vol (Gamma\ X)^0.986. Il n'y a qu'un nombre fini de réseaux arithmétiques de covolume borné par une constante donc ce résultat implique la convergence Benjamini-Schramm pour des variétés arithmétiques de congruence. On donne aussi une version de (\ref{AbsFr1}) un peu plus faible qui reste vraie pour des réseaux arithmétiques qui ne sont pas de congruence. Les majorations de volume de la partie $R$-mince sont déduites d'une version forte de la propriété de la multiplicité limite satisfaite par les réseaux arithmétiques de PGL(2,R) et PGL(2,C). En utilisant nos résultats on confirme la conjecture de Gelander pour des 3-variétés arithmétiques hyperboliques: pour chaque telle variété M on construit un complexe simplicial N homotope à M dont le nombre des simplexes est O(Vol(M)) et le degré des nœuds est uniformément borné par une constante absolue. Dans la deuxième partie on s'intéresse aux espaces localement symétriques Gamma\X où X est de rang supérieur ou égal à 2. Notre résultat principal affirme que la dimension du premier groupe d'homologie à coefficients dans F_2 (corps avec 2 éléments) est sous-linéaire en le volume. Ce résultat est à comparer avec des travaux de Calegari et Emerton sur la cohomologie mod-p dans les tours p-adiques des 3-variétés et les résultats d'Abert, Gelander et Nikolov sur le rang des sous-groupes d'un réseau de rang supérieur à angles droits. Le point fort de notre approche est qu'il n'y a pas besoin de travailler dans une seule classe de commensurabilité. La troisième partie est indépendante des deux premières. Elle porte sur une extension du théorème de Kesten. Le théorème de Kesten affirme que si Gamma est un groupe engendré par un ensemble fini symétrique S, N est un sous-groupe normal de Gamma alors N est moyennable si et seulement si les rayons spectraux du graphe de Cayley Cay(Gamma,S) et du graphe de Scheier Sch(Gamma/N,S) coïncident. En utilisant les techniques de Abert, Glasner et Virag on généralise le theorème de Kesten aux N-uniformément récurrents
Thin groups and superstrong approximation( Book )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

Thin groups and superstrong appriximation by Emmanuel Breuillard( Book )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

Application des marches aleatoires a l'etude des sous-groupes des groupes lineaires by Richard Aoun( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

In this thesis, we use and contribute to the theory of random matrix products in order to study generic properties of elements and subgroups of linear groups. Our first result gives a probabilistic version of the Tits alternative : we show that two independent random walks M_n and M'_n on a non virtually solvable finitely generated linear group will eventually generate a non abelian free subgroup. This answers a question of Guivarc'h and Gilman, Miasnikov and Osin. We show in fact that the probability that M_n and M'_n do not generate a free subgroup decreases exponentially fast to zero. Our methods rely deeply on random matrix products theory. During the proof we give some new limit theorems concerning this theory, some of them will be the generalization of known results for matrices taking value in archimedean fields to arbitrary local fields, others will be new even over R. For example, we show that under natural assumptions on the random walk, the K-parts of M_n in the KAK decomposition become asymptotically independent with exponential speed. Next, we use these properties to study the transience of algebraic subvarieties in algebraic groups. One of our results can be formulated as follows: let H be a non elementary subgroup of SL_2(R), a probability measure with an exponential moment whose support generates H, then for every proper algebraic subvariety V of SL_2(R), the probability that the random walk lies in V decreases exponentially fast to zero. This shows that every proper algebraic subvariety is transient for the random walk. We generalize this result to the case where the support of the probability measure generates a Zariski dense subgroup of the real points of an algebraic group defined and split over R. These results share common flavor with recent works of Kowalski and Rivin
Théorie des groupes approximatifs et ses applications by Arindam Biswas( )

1 edition published in 2016 in French and held by 1 WorldCat member library worldwide

In the first part of this thesis, we study the structure of approximate subgroups inside metabelian groups (solvable groups of derived length 2) and show that if A is such a K-approximate subgroup, then it is K^(O(r)) controlled (in the sense of Tao) by a nilpotent group where r denotes the rank of G=Fit(G) and Fit(G) is the fitting subgroup of G.The second part is devoted to the study of growth of sets inside GLn(Fq) , where we show a bound on the diameter (with respect to any set of generators) for all finite simple subgroups of this group. What we have is - if G is a finite simple group of Lie type with rank n, and its base field has bounded size, then the diameter of the Cayley graph C(G; S) would be bounded by exp(O(n(logn)^3)). If the size of the base field Fq is not bounded then our method gives a bound of q^(O(n(log nq)3)) for the diameter.In the third part we are interested in the growth of sets inside commutative Moufang loops which are commutative loops respecting the moufang identities but without (necessarily)being associative. For them we show that if the sizes of the associator sets are bounded then the growth of approximate substructures inside these loops is similar to those in ordinary groups. In this way for the subclass of finitely generated commutative moufang loops we have a classification theorem of its approximate subloops

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Alternative Names
Emmanuel Breuillard Frans wiskundige

Emmanuel Breuillard fransk matematikar

Emmanuel Breuillard fransk matematiker

Emmanuel Breuillard französischer Mathematiker

Emmanuel Breuillard French mathematician

Emmanuel Breuillard matemático francés

Emmanuel Breuillard mathématicien français

Languages
English (14)

French (9)