87 citations · 292 across the 47 of their papers we have counts for
7 papers · 2 filters
Maximal subgroups of SL(n, Z)
Tsachik Gelander, Chen Meiri
We establish the existence of maximal subgroups of various diferent natures in SL(n,Z). In particular, we prove that there are continuously many maximal subgroups, we provide a max…
Kazhdan-Margulis theorem for Invariant Random Subgroups
Tsachik Gelander
Given a simple Lie group , we show that the lattices in are weakly uniformly discrete. This is a strengthening of the Kazhdan-Margulis theorem. Our proof however is straight…
Rank, combinatorial cost and homology torsion growth in higher rank lattices
Miklos Abert, Tsachik Gelander, Nikolay Nikolov
We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured…
An Upper bound on the growth of Dirichlet tilings of hyperbolic spaces
Itai Benjamini, Tsachik Gelander
It is shown that the growth rate of any faces Dirichlet tiling of the real hyperbolic space is at most , for an , depe…
Higher rank arithmetic groups which are not invariably generated
Tsachik Gelander, Chen Meiri
It was conjectured in [KLS14] that for arithmetic groups, Invariable Generation is equivalent to the Congruence Subgroup Property. In view of the famous Serre conjecture this would…
Infinitesimal generators and quasi non-archimedean topological groups
Tsachik Gelander, François Le Maître
We show that connected separable locally compact groups are infinitesimally finitely generated, meaning that there is an integer such that every neighborhood of the identity co…
A lecture on Invariant Random Subgroups
Tsachik Gelander
Invariant random subgroups (IRS) are conjugacy invariant probability measures on the space of subgroups in a given group G. They can be regarded both as a generalization of normal…