7 problems

Oeding's conjecture. All secant varieties of Segre products of projective spaces are arithmetically Cohen–Macaulay; equivalently, $\widehat{\sigma}_r$ is Cohen–Macaulay for every…

Let $A\in\operatorname{ASM}(n)$ be an alternating sign matrix, and let $1\oplus A\in\operatorname{ASM}(n+1)$ be the direct sum of the $1\times1$ identity matrix with $A$. Cohen–Mac…

Cohen–Macaulayness conjecture. The poset $\operatorname{\mathcal{S}}((V,\Psi),\mathbin{\perp})$ is Cohen–Macaulay.

Let $G$ be a finite simple graph on vertex set $[n]$. For $S\subseteq[n]$, let $c_G(S)$ be the number of connected components of $G-S$, and call $S$ a cut set if…

Consider monomial ideals generated according to the Erdős–Rényi model, with both the number of variables and the degree of the generators tending to infinity. De Loera et al.'s con…

Let random monomial ideals be generated in the Erdős–Rényi model, with the number of variables tending to infinity while the degree of the generators remains fixed. De Loera et al.…

Let $R$ be the polynomial ring containing $x_1,\ldots,x_n$, and let … where $0<b<a$. Uniform-case conjecture. The Rees algebra $\mathcal{R}_R(I)$ is almost Cohen–Macaulay and is Co…