3 problems

Let $X$ be an affine variety of dimension at least $2$, and let … be generated by finitely many ${\mathbb G}_a$-subgroups. Suppose that $G$ acts $2$-transitively on one of its orbi…

Rosenberger's conjecture. If $G$ is a generalised triangle group, then either $G$ is virtually solvable or $G$ contains a non-abelian free subgroup.

Let $M$ be a compact manifold and let $\Gamma$ be a finitely generated group of smooth diffeomorphisms of $M$. Ghys's alternative conjecture. Either $\Gamma$ contains a free group…