collaborators

7 papers

math.DS2026

Generalization of Selberg's theorem for geometrically finite thin subgroups of

Pratyush Sarkar

Let be a geometrically finite thin subgroup of an arithmetic lattice and consider the congruence covers of . In the break…

math.DS2026

Exponential prime orbit theorems for Anosov subgroups

Michael Chow, Pratyush Sarkar

Let be a Zariski dense Anosov subgroup of a connected semisimple real algebraic group -- these are higher rank analogues of convex cocompact subgroups. Let us measure the Jord…

math.DS2026

A dynamical proof of non-arithmeticity of Jordan spectra

Hee Oh, Pratyush Sarkar

We give a dynamical proof of Benoist's non-arithmeticity theorem for Jordan spectra of Zariski dense subgroups of connected semisimple real algebraic groups. After passing to a Zar…

math.DS2026

Strong spectral gap for geometrically finite hyperbolic manifolds

Dubi Kelmer, Osama Khalil, Pratyush Sarkar

Let for be a Zariski dense, geometrically finite, discrete subgroup with critical exponent strictly greater than . We show that…

math.DS2026

Effective equidistribution of translates of tori in arithmetic homogeneous spaces and applications

Pratyush Sarkar

Let be an arithmetic lattice in a noncompact connected semisimple real algebraic group. For many such of rank at most , in particular $G = \operatorname{SL}_3(\mathb…

math.NT2025

Congruence counting in Schottky and continued fractions semigroups of

Pratyush Sarkar

In this paper, the two settings we are concerned with are a Zariski dense Schottky semigroup and a Zariski dense…