8 problems

Let $S$ be a closed oriented surface, let $\rho$ be a Hitchin representation, and let $e_\rho$ denote its energy functional on Teichmüller space. Nondegeneracy conjecture. The mini…

Hitchin–Goldman conjecture. The function $e$ has a unique minimum.

Finite-index Anosov representation conjecture. There exists a finite-index subgroup $\Gamma'$ of $\Gamma$ containing $w$ such that

Anosov density conjecture. The representation $\rho$ is discrete and faithful if and only if it lies in the closure of the space of Anosov representations in…

Let $\Sigma$ be a closed oriented surface and let $(\mathrm{G},\mathrm{P}^\mathbb{R}_\Theta)$ admit a $\Theta$-positive structure. A representation…

Anosov combination conjecture. If each $\Gamma_i$ is $P_{{\tau_{\mathrm{mod}}}}$-Anosov and, for every $i=1,\ldots,n$ and every $\gamma\in\Gamma_i-\{1\}$,

Guichard-Wienhard equivalence. There are connected components of $\operatorname{Hom}(\pi_1(S),G)/G$ which are not distinguished by characteristic invariants if and only if there ex…

Let $\rho: \Gamma\to\operatorname{SO}_{0}(2,n)$ be a GHC-regular representation. A representation is quasi-Fuchsian if it is a deformation of the inclusion of a lattice in…