3 problems

Let $B$ be a mutation matrix, let $(\mathbb A_{B^T},\mathbb Y_B)$ be the associated Fock–Goncharov dual pair, and let $\Theta(\mathbb A_{B^T})$ and $\Theta(\mathbb Y_B)$ denote the…

Let $B$ be an $r\times r$ mutation matrix, and consider the Fock–Goncharov dual pair $(\mathbb A_{B^T},\mathbb Y_B)$. Write $\mathcal U(\mathbb A_{B^T})$ and…

Tropical parametrization conjecture. The basis $\mathbb{I}_{\mathcal{X}}^q(\mathcal{L}_{\mathfrak{sl}_3}^p(Sigma,\mathbb{Z}))$ is parametrized by tropical points. Namely, for every…