6 problems

Let $G$ be the fundamental group of a complex hyperplane arrangement, let $\theta_n(G)$ denote its Chen ranks, and let $\mathcal{R}^1(G;\mathbb{C})\subseteq H^1(G;\mathbb{C})$ be i…

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 $k\ge 3$,

Effective Chen ranks conjecture. For $n\geq 6$ and a general $(2n-2)$-dimensional subspace $K\subseteq\bigwedge^2 V$, one has

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…