A. Golsefidy

activity

20112024

most citedExpansion in perfect groups

38 citations · 87 across the 12 of their papers we have counts for

collaborators

17 papers

math.GR2024

Spectral Independence

Alireza S Golsefidy, Keivan Mallahi-Karai, Amir Mohammadi

We prove the spectral gap property for random walks on the product of two non-locally isomorphic analytic real or p-adic compact groups with simple Lie algebras, under the necessar…

math.GR2020

Locally Random Groups

Keivan Mallahi-Karai, Amir Mohammadi, Alireza Salehi Golsefidy

In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random grou…

math.GR2019

Towards super-approximation in positive characteristic

Brian Longo, Alireza Salehi Golsefidy

In this note we show that the family of Cayley graphs of a finitely generated subgroup of $GL_{n_{0}} (F_{p} (t))$ modulo some admissible square-free polynomials is a fami…

math.GR2018

Diameter of homogeneous spaces: an effective account

Amir Mohammadi, Alireza Salehi Golsefidy, François Thilmany

In this paper we prove explicit estimates for the size of small lifts of points in homogeneous spaces. Our estimates are polynomially effective in the volume of the space and the i…

math.GR2018

Inducing Super-Approximation

Alireza Salehi Golsefidy, Xin Zhang

Let $Γ_{2} \subseteq Γ_{1}$ be finitely generated subgroups of $GL_{n_{0}} (Z [1/ q_{0}])$ . For $i = 1$ or $2$ , let $G_{i}$ be the Zariski-closure of $Γ_{i}$ in $({\rm GL}_{n…

math.DS2016

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…

math.GR2016★ 4 cited

Super-approximation, II: the p-adic and bounded power of square-free integers cases

Alireza Salehi Golsefidy

Let $Ω$ be a finite symmetric subset of GL $_{n} (Z [1/ q_{0}])$ , and $Γ := ⟨ Ω ⟩$ . Then the family of Cayley graphs ${Cay (π_{m} (Γ), π_{m} (Ω))}_{m}$ is a family of expan…

math.GR2016★ 4 cited

Super-approximation, I: p-adic semisimple case

Alireza Salehi Golsefidy

Let $k$ be a number field, $Ω$ be a finite symmetric subset of $GL_{n_{0}} (k)$ , and $Γ = ⟨ Ω ⟩$ . Let \[ C(Γ):=\{\mathfrak{p}\in V_f(k)|\hspace{1mm} Γ\text{is a boun…

math.CO2016

Sum-product phenomena: p-adic case

Alireza Salehi Golsefidy

The sum-product phenomena over a finite extension K of $Q_{p}$ is explored. The main feature of the results is the fact that the implied constants are independent of $p$ .

math.GR2015

Local spectral gap in simple Lie groups and applications

Rémi Boutonnet, Adrian Ioana, Alireza Salehi Golsefidy

We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action…

math.DS2013

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…

math.NT2011

Affine Sieve

Alireza Salehi Golsefidy, Peter Sarnak

We establish the main saturation conjecture in [BGS10] connected with executing a Brun sieve in the setting of an orbit of a group of affine linear transformations. This is carried…

math.NT2011★ 26 cited

S-Arithmetic Khintchine-Type Theorem

Amir Mohammadi, Alireza Salehi Golsefidy

In this article we prove a convergence S-arithmetic Khintchine-type theorem for product of non-degenerate v-adic manifolds, where one of them is the Archimedian place.

math.GR2011★ 11 cited

Lattices of minimum covolume in Chevalley groups over local fields of positive characteristic

Alireza Salehi Golsefidy

In this article, we show that if G is a simply connected Chevalley group of either classical type of rank bigger than 1 or type E6, and q > 9 is a power of a prime number p > 5, th…

math.NT2011

Simultaneous Diophantine Approximation in Non-degenerate p-adic Manifolds

Amir Mohammadi, Alireza Salehi Golsefidy

S-arithmetic Khintchine-type theorem for products of non-degenerate analytic p-adic manifolds is proved for the convergence case. In the p-adic case the divergence part is also obt…

math.GR2011★ 4 cited

Counting lattices in simple Lie groups: the positive characteristic case

Alireza Salehi Golsefidy

In this article we prove a conjecture of A. Lubotzky: let G = G_0(K), where K is a local field of characteristic p>5, G_0 is a simply connected, absolutely almost simple K-group of…

math.GR2011★ 38 cited

Expansion in perfect groups

Alireza Salehi Golsefidy, Péter P. Varjú

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit eleme…