Let G be a connected semisimple real algebraic group, and Γ< G a Zariski dense Anosov
subgroup with respect to a minimal parabolic subgroup. We describe the asymptotic …

Let G:= SO (n, 1)◦ and< G be a geometrically finite Zariski dense subgroup with critical
exponent δ greater than (n− 1)/2. Under a spectral gap hypothesis on L2 (\G), which is …

We prove effective equidistribution, with polynomial rate, for large closed orbits of
semisimple groups on homogeneous spaces, under certain technical restrictions (notably …

For a locally compact second countable group G and a lattice subgroup Γ, we give an
explicit quantitative solution of the lattice point counting problem in general domains in G …

Let $ G $ be the identity component of $\mathrm {SO}(n, 1) $, $ n\ge 2$, acting linearly on a
finite-dimensional real vector space $ V $. Consider a vector $ w_0\in V $ such that the …

Consider a finite system of polynomial equations with integral coefficients. Its set of solutions
defines an arithmetic variety Z⊂ Cd defined over Z. For a set S of primes including the …

We establish asymptotic formulas for volumes of height balls in analytic varieties over local
fields and in adelic points of algebraic varieties over number fields, relating the Mellin …

A geometric transition is a continuous path of geometric structures that changes type,
meaning that the model geometry, ie, the homogeneous space on which the structures are …

We consider the evolution of a compact segment of an analytic curve on the unit tangent
bundle of a hyperbolic n-manifold of finite volume under the geodesic flow. Suppose that the …

We establish that the optimal bound for the size of the smallest integral solution of the
Oppenheim Diophantine approximation problem $| Q (x)-\\xi|<\\epsilon $ for a generic …