10 problems

Gershnik et al.'s conjecture. Every totally extremal normalized ideal Perron similarity is the character table of a finite Abelian group.

Character-table conjecture. If $S$ is a normalized ideal Perron similarity and $S$ is totally extremal, then $S$ is the character table of a finite Abelian group.

Let $\mathbb{SL}_1^n$ denote the normalized set of spectra under consideration, let $\partial \mathbb{SL}_1^n$ be its boundary, and let $\mathbb{E}^n$ be its set of extremal points…

Integer-scaling criterion. If $\{\frac{\lambda_1}{\alpha_1},\ldots,\frac{\lambda_n}{\alpha_n}\}$ is $C_{\mathbb{Q},3}$-realizable, then it is $C_{\mathbb{Q},3}$-realizable if and o…

Let $\Lambda=\{\lambda_1,\dots,\lambda_n\}\subset\mathbb{C}$ with $n\ge 2$ be a list, let … and let $\Lambda'=\{\mu_1,\dots,\mu_{n-1}\}$ be the list of zeros of $p'$. A list is rea…

Monov's conjecture. If $\Lambda$ is realizable, then

Let (JLL), (TAAMP), and (H) denote the named necessary conditions for a list of numbers to be realizable as the spectrum of a nonnegative matrix. JLL and TAAMP sufficiency conjectu…

For $n\in\mathbb{N}$, let $\Theta_n$ denote the set of possible eigenvalues of $n\times n$ stochastic matrices. Let $\Pi_n$ be the convex hull of the $n$th roots of unity, … Let…

Let $\widehat{\sigma}_t$ denote the spectrum under consideration, and form an augmented spectrum by adding any number of zeros to it. Bound conjecture. The value $t=\frac{1}{3}$ is…

Guo's conjecture. If $\sigma$ is symmetrically realisable, then, for the perturbations under consideration, the list