Poincaré Series of Binary Polyhedral Groups and McKay's Correspondence.
Products of trees, lattices and simple groups.
Proper action on a homogeneous space of reductive type.
Propriétés de mélange du flot des chambres de Weyl des groupes de Ping-Pong
Dans cet article, nous étudions le flot des chambres de Weyl d’une large classe de sous-groupe discrets d’un groupe de Lie semi-simple réel : les groupes de Ping-Pong. Nous montrons que ce flot est mélangeant relativement à la mesure de Patterson-Sullivan ; celle-ci étant infinie en rang , nous précisons cette propriété de mélange en explicitant sa vitesse dans le direction du vecteur de croissance du groupe.
Quantitative spectral gap for thin groups of hyperbolic isometries
Let be a subgroup of an arithmetic lattice in . The quotient has a natural family of congruence covers corresponding to ideals in a ring of integers. We establish a super-strong approximation result for Zariski-dense with some additional regularity and thickness properties. Concretely, this asserts a quantitative spectral gap for the Laplacian operators on the congruence covers. This generalizes results of Sarnak and Xue (1991) and Gamburd (2002).
Quasicrystallographic groups on Minkowski spaces.
Quasiflats with holes in reductive groups.
Quotients compacts des groupes ultramétriques de rang un
Soit l’ensemble des points d’un groupe algébrique semi-simple connexe de rang relatif un sur un corps local ultramétrique. Nous décrivons tous les sous-groupes discrets de type fini sans torsion de qui agissent proprement et cocompactement sur par multiplication à gauche et à droite. Nous montrons qu’après une petite déformation dans un tel sous-groupe agit encore librement, proprement discontinûment et cocompactement sur .
Real projective structures on Riemann surfaces
Regularly related lattices in locally compact groups.
Relative property (T) and linear groups
Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group admits a special linear representation with non-amenable -Zariski closure if and only if it acts on an Abelian group (of...
Remarks on points of approximation of discrete sugroups of U(1,n; C).
Representation growth of linear groups
Let be a group and the number of its -dimensional irreducible complex representations. We define and study the associated representation zeta function . When is an arithmetic group satisfying the congruence subgroup property then has an “Euler factorization”. The “factor at infinity” is sometimes called the “Witten zeta function” counting the rational representations of an algebraic group. For these we determine precisely the abscissa of convergence. The local factor at a finite place...
Représentations d'un groupe faiblement équivalentes à la représentation régulière
Representations with cohomology in the discrete spectrum of subgroups of and Lefschetz numbers
Réseaux arithmétiques et commensurateur d'après G. A. Margulis.
Rigidité forte des espaces riemanniens localement symétriques
Rigidity and cohomology of hyperbolic manifolds
When is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.
Rigidity of group actions
Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group.