Locally finite approximation of Lie groups, I.
Matrix coefficients, counting and primes for orbits of geometrically finite groups
Let and for and when for , we obtain an effective archimedean counting result for a discrete orbit of in a homogeneous space where is the trivial group, a symmetric subgroup or a horospherical subgroup. More precisely, we show that for any effectively well-rounded family of compact subsets, there exists such that for an explicit measure on which depends on . We also apply the affine sieve and describe the distribution of almost primes on orbits of in arithmetic settings....
Maximal semigroups in the divisible hull of lattices in nilpotent Lie groups.
Measures on the geometric limit set in higher rank symmetric spaces
Modular embeddings and rigidity for Fuchsian groups
We prove a rigidity theorem for semiarithmetic Fuchsian groups: If Γ₁, Γ₂ are two semiarithmetic lattices in PSL(2,ℝ ) virtually admitting modular embeddings, and f: Γ₁ → Γ₂ is a group isomorphism that respects the notion of congruence subgroups, then f is induced by an inner automorphism of PGL(2,ℝ ).
Monodromy of hypergeometric functions and non-lattice integral monodromy
Nichteuklidische Gitterpunktprobleme und Gleichverteilung in linearen algebraischen Gruppen.
Non-arithmetic groups in Lobachevsky spaces
Nonarithmetic superrigid groups: Counterexamples to Platonov's conjecture.
Non-cohérence de certains reseaux non-uniformes dans le groupe des isométries de l’espace hyperbolique
Non-minimal modular symbols for GL(n).
Nonstationary normal forms and rigidity of group actions.
Non-vanishing on the first cohomology
Nouvelles approches de la propriété (T) de Kazhdan
Un groupe localement compact a la propriété (T) de Kazhdan si la -cohomologie de tout -module hilbertien est nulle. Cette propriété de rigidité de la théorie des représentations de a trouvé des applications qui vont de la théorie ergodique à la théorie des graphes. Pendant près de 30 ans, les seuls exemples connus de groupes avec la propriété (T), provenaient des groupes algébriques simples sur les corps locaux, ou de leurs réseaux. La situation a radicalement changé ces dernières années :...
N-step nilpotent Lie groups with flat Kirillov orbits
On a quantitative version of the Oppenheim conjecture.
On a variant of Kazhdan's property (T) for subgroups of semisimple groups
Let be an irreducible lattice in a product of simple groups. Assume that has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of in terms of the topology of the dual space of .We use this result to give a new proof for the triviality of the first cohomology group of with coefficients in a finite dimensional unitary representation.
On arithmetic Fuchsian groups and their characterizations
This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.
On differential operators attached to certain representations of classical groups.
On discrete subgroups of Lie groups and elliptic geometric structures.
In this paper we continue the investigation of [7]-[10] concerning the actions of discrete subgroups of Lie groups on compact manifolds.