3 problems

Rigidity conjecture. If $\rho\colon\Gamma\to G$ is maximal, then $G=\operatorname{SU}(p,q)$ with $p\geq nq$, and $\rho$ is a trivial deformation of $\rho_{\mathrm{std}}$, namely

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…