7 problems

Let ${\bf B}$ denote the Boolean semiring, and let $H(G;G_+,G_-)$ be the free ${\bf B}$-Hopf algebras introduced in Section 2, associated with the indicated data $G$, $G_+$, and…

Let $\mathcal{P}$ denote the universe of positive bases of intermediate size. A positive basis can be partitioned into minimal sub-positive bases together with critical vectors; th…

Let $\mathbb{D}_{n,s}$ be an optimal positive basis of intermediate size over $\Omega$, partitioned into minimal sub-positive bases and critical vectors as described in the paper.…

Positivity conjecture. Both $(\hat{T}_n)$ and $(S_n)$ are positive on every surface $\Sigma$ with negative Euler characteristic.

Thurston's conjecture. If $\Sigma$ has negative Euler characteristic, then the sequence $(S_n)$ is positive.

Let $\mathcal{S}$ be an oriented surface of finite type, let $\mathcal{S}\mathrm{Web}_q$ be its skein algebra, and let $\mathcal{S}\mathrm{B}_T$ be the basis used in the paper. Pos…

Let ${\mathcal B}^\circ$ and ${\mathcal B}$ denote the bracelet and bangle bases, respectively, for a cluster algebra arising from a marked surface. A basis is positive if the stru…