6 problems

Let ${\mathbb F}={\mathbb R}$, let $A\in{\mathbb F}^{n\times n}$ be Lyapunov regular, and define … where $\mathcal{C}(A)$ is the matrix convex invertible cone generated by $A$,…

Local property conjecture. $n$-convexity is a local property, like $n$-monotonicity.

Four-variable matrix-cube optimum conjecture. The optimal value is $\sqrt{13}/2$. This is equivalent to the conjectured optimality of the four-dichotomic-qubit compatibility bound;…

Let $\mathcal D_{A(k)}$ and $\mathcal D_{A(k)}^\square$ be the free spectrahedron and its matrix polar associated with the simplex-plus-line model defined earlier in the paper, and…

A matrix convex set consists of compatible sets of operator tuples at each matrix level, with matrix convex combinations preserving membership; its free extreme points are the nonc…

Let $q$ be the partial Hessian of a symmetric polynomial, let $Z(0,A)$ be the associated middle matrix evaluated at $A\in\mathbb S_n(\mathbb R^g)$, let $\mu_\pm$ denote the number…