Approximate subgroups and super-strong approximation
Group Theory
2014-07-22 v2
Abstract
Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification of approximate subgroups of semisimple algebraic groups over finite fields. We then give a proof of the super-strong approximation for mod quotients via random matrix products and a quantitative version of strong approximation. Some applications to the group sieve are also presented.
Cite
@article{arxiv.1407.3158,
title = {Approximate subgroups and super-strong approximation},
author = {Emmanuel Breuillard},
journal= {arXiv preprint arXiv:1407.3158},
year = {2014}
}
Comments
55 pages. These notes are based on a series of lectures given at the 2013 Groups St. Andrews meeting. To appear in the Proceedings volume