Free subgroups of linear groups: geometry, algebra, and dynamics
In a celebrated paper, J. Tits proved the following fundamental dichotomy for a finitely generated linear group:
Let G be a finitely generated linear group over an arbitrary field. Then either G is virtually solvable, or G contains a free non-abelian subgroup.
Let G be a non-virtually solvable subgroup of a linear group. We will discuss the following problem(s): is it possible to find a free subgroup of G that fulfills additional (topological, algebraic, and dynamical) conditions?