7 problems

Let $G$ be a finite graph with edge set $E(G)$, and let … where the sum runs over spanning trees $T$ of $G$. Let $V(Q_G)$ be the zero scheme of $Q_G$ in $\mathbf A^{E(G)}$, let…

Let $G$ be a finite graph with vertex set $V(G)$) and edge set $E(G)$. For each edge $e$, let $x_e$ be a variable, and define the Kirchhoff polynomial … where the sum runs over spa…

Let $G$ be a graph with loop number $h_G$ and number of edges $n_G$, and suppose that $G$ is log-divergent, meaning … with $h_G,n_G\geq 3$. A graph is duality admissible when it sa…

Let $G_1$ and $G_2$ be primitive log-divergent graphs with graph periods $I_{G_1}$ and $I_{G_2}$. For each finite field size $q$, define the $c_2$-invariant by … where $X_G$ is the…

Let $\Gamma$ be a finite graph with graph hypersurface $X_\Gamma\subset\mathbb P^{n-1}$, and write $Y_\Gamma=\mathbb P^{n-1}\smallsetminus X_\Gamma$ for its projective hypersurface…

The $c_2$ residue conjecture. If $I_{G_1}=I_{G_2}$ for two primitive log-divergent graphs $G_1$ and $G_2$, then

Let $X_\Gamma=\{\Psi_\Gamma=0\}$ be the graph hypersurface associated with a graph $\Gamma$, embedded in its ambient projective space, and let $H$ denote the hyperplane class. Writ…