6 problems

Veselov's conjecture. This Wronskian has simple zeros, except possibly at $x=0$.

Hermite-polynomial upper-bound conjecture. For all $n\in\mathbb{N}^+$ and $x>0$,

For each $d\geq 1$, define the Hermite polynomial by … Let $\mathscr{R}_d$ denote the set of real polynomials of degree $d$ having only real periodic points. Hermite polynomial con…

Felder–Hemery–Veselov conjecture. For every doubled partition $\lambda=(\mu_1^2,\dots,\mu_n^2)$, $H_\lambda$ has no real roots and has as many imaginary roots as there are odd numb…

Let $\nu=(\mu_1^2,\dots,\mu_n^2)$ be a doubled partition with distinct parts, where $\mu_i^2$ denotes that the part $\mu_i$ occurs twice, and let $W_{\nu}(z)$ be its associated Wro…

Let $\lambda$ be a partition, and let $W_{\lambda}(z)$ denote the Wronskian of Hermite polynomials associated with $\lambda$. Simple-zero conjecture. For every partition $\lambda$,…