8 problems

Generic local-system cohomology conjecture. For every $p$ and almost all $a\in A_1^*$ among those with

Line-closed matroid–quadratic Orlik–Solomon conjecture. $G$ is line-closed if and only if $A(G)$ is quadratic.

Let $\mathcal{L}$ be a geometric lattice. Let $\mathrm{OS}(\mathcal{L})$ be its Orlik–Solomon algebra, and let $\mathbb{I}_{\mathcal{L}}$ be the map defined in the source. Quasi-is…

Let $\mathcal{L}$ be a geometric lattice, and let $\mathrm{OS}(\mathcal{L})$ be its Orlik–Solomon algebra. Orlik–Solomon Koszulness conjecture. The algebra…

Orlik–Solomon strong log-concavity conjecture. The Orlik–Solomon algebra $A(M)$ and the reduced Orlik–Solomon algebra $B(M)$ are strongly equivariantly log concave.

Let $W$ be a finite Coxeter group generated by a set $S$ of simple reflections. Let $\Phi_S$ and $\Psi_S$ denote the characters of the top components of the group algebra…

Let $W$ be a finite real reflection group acting on $V$, let $\mathcal{O}_X$ be a $W$-orbit of intersection subspaces, and let ${{\operatorname{WH}}}_{\mathcal{O}_X}$ be the corres…

Let $A$ be a hyperplane arrangement in $\mathbb{C}\mathbb{P}^n$, and let $V$ be an $n$-isotropic subspace of its Orlik–Solomon algebra of dimension $d\geq n$ that is not contained…