4 problems

Farb–Schwartz conjecture. Commensurator rigidity, or at least the weaker statement, should hold for nonuniform lattices in a wide class of Lie groups: two such lattices are quasi-i…

Farb's quasi-isometric rigidity conjecture. There exists a homomorphism

Rigidity conjecture for $\operatorname{Solv}$. The group $\operatorname{Solv}$ is quasi-isometrically rigid: every finitely generated group $G$ quasi-isometric to…

Random Menger-boundary discreteness conjecture. We conjecture that, generically—for random groups—hyperbolic groups with Menger curve boundary are graphically discrete.