5 problems

The weighted derivative-substitution conjecture. This mapping determines a map

The scalar strong BMV coefficient conjecture. Every $f_i$ belongs to $\mathbf{P}^{\mathrm{pos}}$, and consecutive coefficients satisfy

Let $A$ and $B$ be positive definite matrices, and let $n$ be a positive integer. The BMV conjecture. The polynomial in $t$ … has all positive coefficients. The source presents thi…

Structure-coefficient positivity conjecture. For all $F,G,H\in L(M)$, $C_{FG}^H(q)\in\mathbb{N}[q]$. The conjecture was disproved by examples in rank $4$ and higher, including a un…

Let $P_{3,6}$ be the cone of nonnegative ternary sextic forms, let $\Delta_{3,6}$ be its relevant cone of forms under consideration, and let $E(P_{3,6})$ denote the set of extremal…