Workshop on Thin Groups and Super Approximation

In this talked we will explain how the classical large sieve method from number theory can be applied to study properties of subsets of groups which have property-τ . As an application we will show that the set of powers in finitely-generated non-...

In this talk the general setting of affine sieve will be presented. Next I will explain the Bourgain-Gamburd-Sarnak method on proving affine sieve in the presence of certain spectral gap. Finally I will say how one can prove the fundamental theorem...

I will explain the Bourgain-Gamburd method of proving spectral gap. The spirit of this method is behind all the recent results on this subject. Very roughly it says in order to prove spectral gap it is enough to show that a “generic” subset with...

Abstract: Let Γ be a finitely generated subgroup of a compact group G. 1. I will recall what it means to say the action of Γ on G by left translation has spectral gap, and mention some examples and applications, e.g. Banach-Ruziewicz problem...

Schedule: https://sites.google.com/site/thingroups/schedule

In this talk we introduce the Apollonian group, sometimes coined the “quintessential” thin group, which is the underlying symmetry group of Apollonian circle packings. We review some of...