3 problems

Terminal stability conjecture. For each fixed $r\ge2$ there exists a finite list of square multigraphs $G_1,\ldots,G_N$, depending only on $r$ and not on $n$, such that for all…

Square-graph cone conjecture. For every $n\ge2$ and every $0\le k\le n-2$, the polynomial $\mathcal D_k^{(n)}$ belongs to the square-graph cone. Equivalently, $\mathcal D_k^{(n)}$…

Let $p$ and $q$ be degree-$d$ polynomials, let $p\boxplus_d q$ denote their finite free convolution, and let $\operatorname{Dis}(p)$ denote the discriminant of $p$. Minkowski inequ…