9 problems

Let ${\mathcal A}$ be a central hyperplane arrangement, let $M({\mathcal A})$ be its complement, and let ${\mathcal R}^1({\mathcal A})$ denote the first resonance variety of…

Suciu's conjecture. For every hyperplane arrangement $A$, this Chen rank formula holds for all sufficiently large $q$. The source records this as a conjectural extension of the sta…

Resonance Chen-group formula. For $k\ge 3$,

Let $\mathcal{A}$ be a complex hyperplane arrangement with arrangement group $G=G(\mathcal{A})$. Let $R_1(\mathcal{A})=\bigcup_i L_i$ be its resonance variety, and set…

Let $\mathcal{A}$ be a complex hyperplane arrangement with arrangement group $G=G(\mathcal{A})$. Write the resonance variety as $R_1(\mathcal{A})=\bigcup_i L_i$, where the $L_i$ ar…

Let $\mathsf{M}$ be a simple matroid. For each sub-matroid $\mathsf{M}'\subset \mathsf{M}$, let $n_k(\mathsf{M}')$ be the number of $k$-multinets supported by $\mathsf{M}'$, and le…

Reduced projective resonance and Chen ranks conjecture. The projective resonance ${\bf R}(G)$ of any Kähler group $G$ is reduced. Moreover, if $X$ is a compact Kähler manifold, the…

Higher-depth resonance decomposition conjecture. For $d\geq 2$, this inclusion is an equality and the displayed union gives the decomposition into irreducible components of…

Let ${\mathcal{A}}$ be a hyperplane arrangement, let $A$ be its Orlik–Solomon algebra, and define the first resonance variety by … A neighborly partition is a partition of…