4 problems

Sagan–Swanson's conjecture. The set of monomials ${\mathcal{A}}_{n,r}$ descends to a vector space basis of $SR_{n,r}$.

Proposed colored-face model. The ideal $SI'_{n,r}$ is stable under ${\mathbb{Z}}_r\wr{\mathfrak S}_n$, and there is a module isomorphism

Murai–Rhoades–Wilson's conjecture. There exists a $G$-equivariant surjection

Murai–Rhoades–Wilson's conjecture. For every $d\geq 0$, there exists a $G$-equivariant surjection