7 problems

Iterated-derivative toric-residue conjecture. A rational $A$-hypergeometric function has an iterated derivative that is a linear combination of toric residues associated with facia…

Essential Cayley facial subset conjecture. If $A$ admits a rational $A$-hypergeometric function that is not a Laurent polynomial, then $A$ has a facial subset that is an essential…

Let $d\in\mathbb{N}_+$, and define … where $\mathbb{S}^{d-1}$ is the unit sphere in $\mathbb{R}^d$ and $\|\cdot\|_2$ is the standard Euclidean norm. Ambrus–Nietert's conjecture. ……

Generalized upper bound conjecture for sublevels. Then

Small $g$-matrix nonnegativity conjecture. The small $g$-matrix of every vector configuration in $\mathbb{R}^r$ is nonnegative.

Covector codegree decomposition conjecture. Every irreducible vector configuration $\boldsymbol{\mathbf{V}}$ of rank $r$ admits a codegree${}^{\star}$ decomposition of length at le…

Marcus's conjecture. The maximum size of a minimal positively $k$-spanning configuration in $\mathbb{R}^m$ is $2km$.