61 citations · 200 across the 32 of their papers we have counts for
20 papers · 1 filter
Cosets with constant characteristic polynomial
Nir Avni, Tsachik Gelander
Let H be a linear group. We show that if there is an invertible matrix x such that all the elements of xH share the same characteristic polynomial then H is virtually solvable. The…
Mixed identities in linear groups -- effective version
Nir Avni, Tsachik Gelander
We show that MIF (mixed-identity-free) linear groups are sharply MIF and linearly MIF. Along the way we provide a self contained proof of the strong approximation theorem, and a ne…
Bounded Generation for
Nir Avni, Chen Meiri
Let be an order in a division algebra over a number field. We prove, under some conditions, that is boundedly generated by elementary matrices.
Fourier and small ball estimates for word maps on unitary groups
Nir Avni, Itay Glazer, Michael Larsen
To a non-trivial word in a free group on elements and a group , one can associate the word map that takes an -tupl…
Conjugacy width in uniform higher rank arithmetic groups of orthogonal type
Nir Avni, Chen Meiri
We study widths of conjugacy classes in anisotropic higher rank -arithmetic groups of orthogonal type. Assuming the GRH, we prove that many such groups have bounded conjugacy wi…
Is being a higher rank lattice a first order property?
Nir Avni, Chen Meiri
We show that there is a sentence in the first order language of groups such that a finitely generated group satisfies if and only if is isomorphic to a group of the…
On the model theory of higher rank arithmetic groups
Nir Avni, Chen Meiri
Let be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if is either non-uniform or is uniform of orthogonal type and dimension…
Words have bounded width in
Nir Avni, Chen Meiri
We prove two results about width of words in . The first is that, for every , there is a constant such that the width of any word in $SL_n(\mathb…
First order rigidity of non-uniform higher rank arithmetic lattices
Nir Avni, Alexander Lubotzky, Chen Meiri
If is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example, , ) and is a finitely generated group that is…
Counting points of schemes over finite rings and counting representations of arithmetic lattices
Avraham Aizenbud, Nir Avni
We relate the singularities of a scheme to the asymptotics of the number of points of over finite rings. This gives a partial answer to a question of Mustata. We use this r…
Similarity classes of integral -adic matrices and representation zeta functions of groups of type
Nir Avni, Benjamin Klopsch, Uri Onn +1
We compute explicitly Dirichlet generating functions enumerating finite-dimensional irreducible complex representations of various -adic analytic and adelic profinite groups of…
Word Values in p-Adic and Adelic Groups
Nir Avni, Tsachik Gelander, Martin Kassabov +1
We study the sets of values of words in p-adic and adelic groups.
Arithmetic groups, base change, and representation growth
Nir Avni, Benjamin Klopsch, Uri Onn +1
Consider an arithmetic group , where is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over t…
Representation zeta functions of some compact p-adic analytic groups
Nir Avni, Benjamin Klopsch, Uri Onn +1
Using the Kirillov orbit method, novel methods from p-adic integration and Clifford theory, we study representation zeta functions associated to compact p-adic analytic groups. In…
Representation zeta functions of compact p-adic analytic groups and arithmetic groups
Nir Avni, Benjamin Klopsch, Uri Onn +1
We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups. They allow us t…
On representation zeta functions of groups and a conjecture of Larsen and Lubotzky
Nir Avni, Benjamin Klopsch, Uri Onn +1
We study zeta functions enumerating finite-dimensional irreducible complex linear representations of compact p-adic analytic and of arithmetic groups. Using methods from p-adic int…
On Commensurizer Growth
Nir Avni, Seonhee Lim, Eran Nevo
We study new asymptotic invariant of a pair consisting of a group and a subgroup, which we call Commensurizer Growth. We compute the commensurizer growth for several examples, conc…
Arithmetic Groups Have Rational Representation Growth
Nir Avni
Let G be an arithmetic lattice in a semisimple algebraic group over a number field. We show that if G has the congruence subgroup property, then the number of n-dimensional irreduc…
Connectivity of the Product Replacement Graph of Simple Groups of Bounded Lie Rank
Nir Avni, Shelly Garion
The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertic…
Similarity classes of 3x3 matrices over a local principal ideal ring
Nir Avni, Uri Onn, Amritanshu Prasad +1
In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for…