9 problems

Baker–Jin conjecture.

Hypothesis R. Every null root of every polynomial over $(\mathcal A,\mathcal A_0)$ is a factor-root.

Let $d,n$ be positive integers. Write ${\mathbb P}\operatorname{L}(d,n)_{\boxtimes}$ for the space of square-free Lorentzian polynomials of degree $d$ in $n$ variables modulo posit…

Strong minimality conjecture. A hyperfield is strongly minimal if and only if it is either a strongly minimal field, that is, an algebraically closed field, or a hyperfield whose h…

Krasner's conjecture. Every hyperfield is a factor hyperfield of this form. The construction is known to produce a hyperfield for every field and subgroup, but the source provides…

Inheritance-property conjecture. All hyperfields with the doubly distributive property satisfy the inheritance property.

Multiplicity-bound conjecture. All hyperfields with the doubly distributive property satisfy the multiplicity bound.

Let $n$ be a positive odd integer, and let a generating set be a set of positive integers generating the characteristic of a hyperfield. Existence conjecture. For every positive od…

Weak Closure Property. The Weak Closure Property holds for all matroids over hyperfields. This would characterize a broad class of tract-like coefficient systems for which vector s…