6 problems

Visibility Density Conjecture. If $F(x)\in\mathbb{Z}[x]$ has at least two distinct roots, then the set of lattice points in $\mathbb{Z}_{>0}\times\mathbb{Z}_{>0}$ visible along…

Visibility-dimension claim. This element is not visible in any abelian threefold; in particular, its visibility dimension is $4$.

Two 1-visibility cops cleaning conjecture. Two 1-visibility cops can clean at least $10$ vertices of $G$, or they can clean the whole graph.

Let $S\subseteq\mathbb{Z}^k$ be a finite set, and let $V(S)$ denote the set of lattice points mutually visible from every point of $S$. Write $D(V(S))$ for its asymptotic density a…

Jetchev–Stein conjecture. Every class in $\Sh(E/\mathbf{Q})$ is modular.

Three-color guarding conjecture. Every simple polygon admits a weak conflict-free vertex-to-vertex chromatic guarding with at most $3$ colors.