5 problems

Let $n\geq 3$ and consider extremizers of the $p$-Stam inequality among normalized monic real-rooted polynomial pairs $(f,g)$ of degree $n$; write $d_{PQ}$ for their pair mismatch…

For each $n\geq 3$, consider the $p$-Stam inequality for monic real-rooted pairs of degree $n$, with critical exponent denoted by $p^*$. $p$-Stam phase transition conjecture. For a…

Let $n\geq 3$, let $h\in\mathbb{R}^n$ be the normalized Hermite root vector, and define … Let $W=\mathbf{1}^\perp=\{u\in\mathbb{R}^n:u^\top\mathbf{1}=0\}$ be the mean-zero subspace…

For each $d\geq 1$, let $\Phi_d$ be the limiting-polynomial map associated with finite free multiplicative convolution, and let $\Phi$ be the map characterized by the free multipli…

Rank-two permanent inequality. For any matrix $T$ with rank at most $2$,