Emmanuel BREUILLARD : On the Tits Alternative and its Refinements 

I shall present Tits' original statement and method of proof
of his celebrated alternative for finitely generated linear groups
and present various efinements that have been obtained over the years
as well as open problems. In particular, I shall discuss the notion of strongly
dense free subgroup appearing in recent joint work with Guralnick
and Larsen on this topic as well as connections to the study of word maps
and expander graphs.