11 problems

Let $(\Sigma,[g])$ be a Riemann surface with marked points, let $\mathcal{M}_{\mathfrak{g},m}$ be its moduli space, and let $\mathcal{T}_{\mathfrak{g},m}$ be Teichmüller space, the…

Faddeev's conjecture. The constant part of the inversion factor on the right-hand side, namely $\exp\left(-\frac{\mathsf i\pi}{12}(\lambda^2+\lambda^{-2})\right)$, is related to th…

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 $G$ be a complex semisimple Lie group, $S$ a marked surface, $c$ a simple closed curve on $S$, and $V$ a finite-dimensional representation of $G$. Let $\mathbb L_{G,S}$ be the…

Let $\mathfrak{S}$ be a punctured surface with at least one puncture. The projected ${\rm SL}_n$-skein algebra is the quotient … where $\mathcal K_{\hat\omega,\mathfrak{S}}$ is the…

Let $\mathcal{F}_igma$ be the space of coefficient tuples for a surface $igma$, let $phi in MC(igma)$ be a mapping class, and let ${\boldsymbol{p}}_igma in \mathcal{F}_sigma$ be…

Let $\mathfrak{S}$ be a triangulable marked surface. A pants triple $(\gamma,\gamma_1,\gamma_2)$ is a triple of loops of the type defined in the paper, and a Teschner triple of a g…

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…

Let $\mathbf{\Sigma}=(\Sigma,\mathcal{P})$ be a closed punctured surface and let $\omega$ be a non-zero complex number. The stated skein algebra…

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