4 problems

Ren–Xu's conjecture. If the Hilbert series of $Q_m(n,\mathbf{F}_p)$ differs from that of $Q_m(n,\mathbf{Q})$, then there exist integers $a\geq 0$ and $k\geq 0$ satisfying the displ…

Let $m$ and $n$ be positive integers, let $q$ be a nonzero complex number, and let $Q_{m,q}(n)$ and $Q_m(n,\mathbb{C})$ denote the $q$-deformed and ordinary $m$-quasi-invariant pol…

Let $m$ be a nonnegative integer, let $f_1,f_2,\dots,f_n$ be one-variable meromorphic functions, and let $Q_m(f_1,\dots,f_n)$ be the space of polynomials…

Let $Q_m(n)$ denote the space of quasi-invariant polynomials in $n$ variables with parameter $m$, and let $p$ be prime. Suppose the Hilbert series of $Q_m(n)$ over $\mathbb F_p$ di…