41 citations · 81 across the 15 of their papers we have counts for
13 papers · 1 filter
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 breakthr…
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…
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…
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(\mathbb…
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 Jorda…
Finitary estimates for the distribution of lattice orbits in homogeneous spaces I: Riemannian metric
Zuo Lin, Pratyush Sarkar
Let both be noncompact connected semisimple real algebraic groups where the former is maximal proper and be a lattice. Building on the work of Gorodnik-Weiss, we ref…
Exponential mixing of frame flows for geometrically finite hyperbolic manifolds
Jialun Li, Wenyu Pan, Pratyush Sarkar
As a final work to establish that frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions are exponentially mixing with respect to the Bowen-Margulis-Sull…
Exponential mixing of frame flows for convex cocompact locally symmetric spaces
Michael Chow, Pratyush Sarkar
Let be a connected center-free simple real algebraic group of rank one and be a Zariski dense torsion-free convex cocompact subgroup. We prove that the frame flow on $Γ\…
Local mixing of one-parameter diagonal flows on Anosov homogeneous spaces
Michael Chow, Pratyush Sarkar
Let be a connected semisimple real algebraic group and be a Zariski dense Anosov subgroup with respect to a minimal parabolic subgroup. We prove local mixing of the one-…
Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps
Jialun Li, Wenyu Pan
Let be a geometrically finite discrete subgroup in with parabolic elements. We establish exponential mixing of the geodesic flow on the unit…
Generalization of Selberg's theorem for convex cocompact thin subgroups of
Pratyush Sarkar
Let be a convex cocompact thin subgroup of an arithmetic lattice in . We generalize Selberg's theorem in this setting, i.e., we prove un…
Exponential mixing of frame flows for convex cocompact hyperbolic manifolds
Pratyush Sarkar, Dale Winter
The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan…
Uniform exponential mixing for congruence covers of convex cocompact hyperbolic manifolds
Pratyush Sarkar
Let be a Zariski dense convex cocompact subgroup contained in an arithmetic lattice of . We prove uniform exponential mixing of the geodesic fl…