3 problems

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…

Let $X$ be a compact Kähler manifold. For each $g\geq 2$, let $\mathcal{E}(X)$ be the set of relevant fibrations $f\colon X\to B_f$ and define … Here $\Pi_g$ denotes the fundamenta…

Let ${\mathcal{A}}$ be a hyperplane arrangement, let $G=G({\mathcal{A}})$ be its arrangement group, and let $R^{1}({\mathcal{A}})$ be its first resonance variety. For each $r$, let…