12 problems

Let the Grünbaum–Cuntz catalogue be the catalogue of known three-dimensional simplicial hyperplane arrangements, consisting of 95 sporadic arrangements and three infinite families.…

Let $\mathcal{A}$ be a simplicial arrangement, and let $P_{\mathcal{A}}(z)$ denote its Primitive Eulerian polynomial. Simplicial-arrangement real-rootedness conjecture. The polynom…

Grünbaum–Cuntz conjecture. Every simplicial arrangement of rank $3$ is isomorphic to an arrangement in the Grünbaum–Cuntz catalog.

Real simplicial-arrangement moduli conjecture. The moduli space of the matroid of a real simplicial arrangement is always finite.

Gruenbaum–Giessen h-vector conjecture. One has

Gruenbaum–Giessen finiteness conjecture. There are only finitely many different isomorphism classes of irreducible simplicial arrangements in $\mathbb{P}^3$.

37-hyperplane conjecture. If $\lvert\mathcal{A}\rvert>37$, then

Let ${\mathcal A}$ be a simplicial real line arrangement, and call it nontrivially monodromic when its Milnor fiber has nontrivial monodromy. The known arrangements referred to in…

Asymptotic classification conjecture. There exists an $N\in\mathbb{N}$ such that the incidence of every simplicial arrangement in $\mathbb{C}^3$ with more than $N$ hyperplanes is i…

Stretchability conjecture. Every simplicial arrangement with at most $14$ pseudolines is stretchable.

Grünbaum's classification conjecture. There are no simplicial arrangements of straight lines besides the three infinite families and $90$ sporadic arrangements listed in Grünbaum's…

Grünbaum's conjecture. Up to isomorphism, there are only $5$ simplicial unstretchable arrangements of $15$ or $16$ pseudolines.