4 problems

Universal positive-basis conjecture. There is a unique vector $c \mathbf{v}_infty$ such that, for every choice of $R$, the $c \mathbf{g}$-vectors of cluster variables for $B^T$, to…

Let $\Lambda$ be a periodic algebra, and let $\mu_\bullet(\Lambda)$ denote its mutation class, consisting of the isoclasses of algebras obtained from $\Lambda$ by finite sequences…

Let $B\in\mathrm{M}_{n}(\mathbb{R})$ be a skew-symmetrizable matrix with skew-symmetrizer $D=\mathrm{diag}(d_1,\dots,d_n)$. Suppose that $B$ satisfies the sign-coherent property, m…

Positivity conjecture. Every triple $(A,B,C)$ of positive integer solutions to the shadow Markoff equation can be obtained from an initial triple with $(\alpha:\beta:\gamma)$ a rat…