4 problems

Let $\mathcal{P}_{n,2n}$ be the cone of polynomials of degree at most $2n$ that preserve nonnegative matrices of order $n$, and let $\mathbf{v}$ denote the coefficient vector of su…

Normalized-volume decay conjecture.

Continuity conjecture. The largest $t\in\mathbb{R}^+$ such that $p_t\in\mathcal{P}_n$ for all such $m,s$ is a continuous function of $m$ and $s$, bounded between $1$ and $2$. The c…

Let $\mathcal{P}_{n,m}$ be the cone of degree-at-most-$m$ polynomials that preserve nonnegative matrices of order $n$, and consider its volume after restriction to the unit sphere.…