4 problems

Let $G=\operatorname{PGL}_{n+1}$, let $S$ be a marked surface, and let $c$ be an essential simple closed curve on $S$. Let $S'$ be obtained by cutting $S$ open along $c$, and let…

Let $\mathfrak{S}$ be a triangulable marked surface and let $\Delta$ be its ideal triangulation. Let $\gamma$ be an essential non-peripheral simple loop, let…

Let $\mathfrak{S} = \Sigma \setminus \mathcal{P}$ be a triangulable marked surface, let $\Delta$ be an ideal triangulation, and let $\hbar \in \mathbb{R}_{>0}$. For an essential si…

Structure-coefficient positivity conjecture. Only finitely many structure coefficients $c^q(\ell,\ell';\ell”)$ are nonzero, and every one belongs to $\mathbb{Z}_{\geq 0}[q,q^{-1}]$…