36 citations · 106 across the 26 of their papers we have counts for
17 papers · 1 filter
An effective version of the Oppenheim conjecture with a polynomial error rate
Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang +1
We prove an effective version of the Oppenheim conjecture with a polynomial error rate. The proof is based on an effective equidistribution theorem which in turn relies on recent p…
Polynomial effective equidistribution
Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang
We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of in arithmetic quotients of $\ope…
Polynomial effective density in quotients of and
Elon Lindenstrauss, Amir Mohammadi
We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of in arithmetic quotients of $\oper…
Benjamini-Schramm convergence of periodic orbits
Amir Mohammadi, Kasra Rafi
We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation…
Quantitative behavior of unipotent flows and an effective avoidance principle
Elon Lindenstrauss, Amir Mohammadi, Gregory Margulis +1
We give an effective bound on how much time orbits of a unipotent group on an arithmetic quotient can stay near homogeneous subvarieties of corresponding to $\math…
Geodesic planes in the convex core of an acylindrical 3-manifold
Curtis T. McMullen, Amir Mohammadi, Hee Oh
Let be a convex cocompact acylindrical hyperbolic 3-manifold of infinite volume, and let denote the interior of the convex core of . In this paper we show that any geo…
Characteristic free measure rigidity for the action of solvable groups on homogeneous spaces
Amir Mohammadi, Alireza Salehi Golsefidy
We classify measures on a homogeneous space which are invariant under a certain solvable subgroup and ergodic under its unipotent radical. Our treatment is independent of character…
On effective equidistribution for quotients of SL(d)
Menny Aka, Manfred Einsiedler, Han Li +1
We prove the first case of polynomially effective equidistribution of closed orbits of semisimple groups with nontrivial centralizer. The proof relies on uniform spectral gap, buil…
Invariant Radon measures for Unipotent flows and products of Kleinian groups
Amir Mohammadi, Hee Oh
Let G=PSL(2, F) where F= R or C, and consider the space Z=(Γ_1 x Γ_2)\ (G x G) where Γ_1<G is a co-compact lattice and Γ_2<G is a finitely generated discrete Zariski dense subgroup…
Closed geodesics and holonomies for Kleinian manifolds
Gregory Margulis, Amir Mohammadi, Hee Oh
For a rank one Lie group G and a Zariski dense and geometrically finite subgroup of G, we establish equidistribution of holonomy classes about closed geodesics for the associat…
Classification of joinings for Kleinian groups
Amir Mohammadi, Hee Oh
We classify all locally finite joinings of a horospherical subgroup action on Γ\ G when Γis a Zariski dense geometrically finite subgroup of G=PSL_2(R) or PSL_2(C). This generalize…
Translate of horospheres and counting problems
Amir Mohammadi, Alireza Salehi Golsefidy
Let G be a semisimple Lie group without compact factors, Γbe an irreducible lattice in G. In the first part of the article we give the necessary and sufficient condition under whic…
Isolation, equidistribution, and orbit closures for the SL(2,R) action on Moduli space
Alex Eskin, Maryam Mirzakhani, Amir Mohammadi
We prove results about orbit closures and equidistribution for the SL(2,R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent fl…
Logarithm laws for one parameter unipotent flows
Dubi Kelmer, Amir Mohammadi
We prove logarithm laws and shrinking target properties for unipotent flows on the homogenous space $Γ\bs G$ with $G=\SL_2(\bbR)^{r_1}\times\SL_2(\bbC)^{r_2}$ and an…
A special case of effective equidistribution with explicit constants
Amir Mohammadi
An effective equidistribution with explicit constants for the isometry group of rational forms with signature is proved. As an application we get an effective discreteness…
Unipotent Flows And Isotropic Quadratic Forms In Positive Characteristic
Amir Mohammadi
The analogous statement to Oppenheim conjecture over a local field of positive characteristic is proved. The dynamical argument is most involved in the case of characteristic 3.
Measures Invariant Under Horospherical Subgroups in Positive characteristic
Amir Mohammadi
We prove measure rigidity for the action of (maximal) horospherical subgroups on homogeneous spaces obtained by quotient by a uniform (nonuniform) arithmetic lattices over a field…