16 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…

Let $Z_{b3,\lambda,d}^{(\lambda)}$ denote the visibility region in hyperbolic $d$-space obtained by observing along a $\lambda$-geodesic ray through a Poisson process of obstructin…

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

Let $P_m$ be the path graph on $m$ vertices and $C_n$ the cycle graph on $n$ vertices. For a graph $G$, let $\mathrm{f}\mu^{(0)}(G)$ denote its fault-tolerant mutual-visibility num…

Let $\mathscr{P}$ be a simple polygon. A witness set for $\mathscr{P}$ is a set of points in $\mathscr{P}$ such that every point of $\mathscr{P}$ is visible from at most one point…

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.

Lower-bound conjecture. We conjecture that

Consider the two-dimensional RPSSL network and its two-dimensional unstable manifold. Two-dimensional RPSSL visibility conjecture. The two-dimensional RPSSL network is visible, bec…

The one-dimensional RPSSL network has trajectories with irregular visits to all parts of the network, together with rare excursions away from the network. Indefinite-excursion conj…

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.

Nonexistence conjecture. There is no spiral set which is a dense forest.

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

Visibility conjecture. For almost all $e\in S^1$,

Higher-level visibility conjecture. Every element of the Shafarevich–Tate group can be explained by visibility at some higher level.

Let $f$ be the newform and $A_f$ the associated modular abelian variety. For an abelian variety $J$ equipped with a map $A_f^\vee\to J$, an element of…