3 problems

Two-sided Curto–Herrero conjecture. For every ${\underline{A}},{\underline{B}}\in M_n^m$, the ${\rm GL}_n$-orbits of ${\underline{A}}$ and ${\underline{B}}$ coincide if and only if

Determinant conjecture. The determinant $|X(t)|$ can be obtained as a component of the solution of a linear system of differential equations with constant coefficients, whose coeff…

Let $p$ be the characteristic of the ground field, let $R^{S\!p(n)}$ be the invariant ring for $n\times n$ generic matrices under the symplectic group, and let $K_{\infty}$ denote…