3 problems

Savini's boundary-map conjecture. Given a Zariski-dense measurable cocycle $\sigma:\Gamma\times X\rightarrow G$, the cocycle has a boundary map.

Twisted diagonal deformation conjecture. If $G$ is not locally isomorphic to $\mathrm{Sp}(2n,\mathbf{R})$, then every maximal representation

Topological invariants conjecture. If $G$ is not locally isomorphic to $\mathrm{Sp}(2n,\mathbf{R})$, then the topological invariants of Theorem distinguish connected components of…