5 problems

Homogeneous glicci conjecture. Every Cohen–Macaulay monomial ideal is homogeneously glicci.

Class G bounds conjecture. If $n=2$, then

Optimal-bounds conjecture. For ideals of class $\mathbf{H}$ with $m\geq 5$ and $n\geq 3$, the established bounds on $p$ and $q$ are optimal.

Let $I$ be a perfect ideal of height $3$ in a Gorenstein local ring $R$ with infinite residue field. For a structure map $w^{(i)}_{j,k}(J)$, write “nonzero modulo the maximal ideal…

Let $R$ be a Gorenstein local ring and let $\mathfrak{f}=(1,m,m+n-1,n)$ be a resolution format realized by some grade $3$ perfect ideal in $R$. A perfect ideal is licci if it belon…