87 citations · 292 across the 47 of their papers we have counts for
62 papers
Counterexamples to the continuous Aldous-Lyons conjecture
Tsachik Gelander
We construct non-co-sofic invariant random subgroups in connected simple real Lie groups of rank one with finite center, in Zariski connected simple rank-one groups over non-Archim…
Small Kazhdan constants for small generating sets of linear groups
Tsachik Gelander, Alex Lubotzky, Jvbin Yao
Let G be a linear group with Kazhdan property (T) generated by d elements. We show that there are generating sets of size d+2 with arbitrarily small Kazhdan constants. We also prov…
Spectral gap for products and a strong normal subgroup theorem
Uri Bader, Tsachik Gelander, Arie Levit
We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a…
Things we can learn by considering random locally symmetric manifolds
Tsachik Gelander
In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a…
An Invitation to Analytic Group Theory
Tal Cohen, Tsachik Gelander
This book is concerned with analytic approaches of studying groups and their actions. Much attention is devoted to the study of amenability and Kazhdan's property (T), which are pe…
A Quantitative Selberg's Lemma
Tsachik Gelander, Raz Slutsky
We show that an arithmetic lattice in a semi-simple Lie group contains a torsion-free subgroup of index where is the co-volume of the lattice. We prove…