Tue, 08 Mar 2016
14:15 -
15:30
L4
Strongly dense subgroups of semisimple algebraic groups.
Emmanuel Breuillard
(Orsay and Munster)
Abstract
A subgroup Gamma of a semisimple algebraic group G is called strongly dense if every subgroup of Gamma is either cyclic or Zariski-dense. I will describe a method for building strongly dense free subgroups inside a given Zariski-dense subgroup Gamma of G, thus providing a refinement of the Tits alternative. The method works for a large class of G's and Gamma's. I will also discuss connections with word maps and expander graphs. This is joint work with Bob Guralnick and Michael Larsen.