Let Γ be a group generated by a finite set S. We give a sufficient condition for Γ to have
Kazhdan's property (T). This condition is easy to check and gives Kazhdan constants. We …

The theory of expander graphs is a rapidly developing topic in mathematics and computer
science, with applications to communication networks, error-correcting codes, cryptography …

Property (T) was introduced in a seminal paper of Kazhdan [104] in 1967. A group G has this
property if the trivial one dimensional representation of G is” bounded away” from all the …

In the mid 60's, D. Kazhdan defined his Property (T) for locally compact groups and used it
as a tool to demonstrate that a large class of lattices are finitely generated. Recall that a …

We prove the following conjecture of Margulis. Let G be a higher rank simple Lie group, and
let Λ≤G be a discrete subgroup of infinite covolume. Then, the locally symmetric space …

We generalize a version of small cancellation theory to the class of acylindrically hyperbolic
groups. This class contains many groups which admit some natural action on a hyperbolic …

We show that for any non-virtually solvable finitely generated group of matrices over any
field, there is an integer m such that, given an arbitrary finite generating set for the group …

This is an exposition of examples and classes of finitely-generated groups which have
uniform exponential growth. The main examples are non-Abelian free groups, semi-direct …

We discuss dense embeddings of surface groups and fully residually free groups in
topological groups. We show that a compact topological group contains a nonabelian dense …

We study some properties of the varieties of deformations of free groups in compact Lie
groups. In particular, we prove a conjecture of Margulis and Soifer about the density of non …