5 problems

Let $G$ be a graph, let $\mathcal{A}_G^q$ be its $q$-deformed graphical arrangement, let $\chi(\mathcal{A}_G^q,t)$ denote the characteristic polynomial of this arrangement, and let…

Let $n$ be fixed, let $a$ vary, and fix a tree of gain functions. Consider the regions of the arrangement $\mathcal{A}^{a,a}_{n-1}$ associated to that tree. Polynomiality conjectur…

The graph-generalized Orlik–Terao conjecture. For any simple connected graph $\Gamma$, there exists an isomorphism

Let $\mathcal{A}_{G,\psi}$ be a $\psi$-graphical arrangement, and call it free when its cone is a free arrangement. Recall that an arrangement is supersolvable when the intersectio…

Let $(G,\psi)$ be a graph together with the data defining its $\psi$-graphical arrangement $\mathcal{A}_{G,\psi}$. Suppose the vertices of $G$ can be ordered as $v_1,\dots,v_p$ so…