8 problems

Transversality criterion. The condition

For a $phi^4$ graph, namely a 4-regular graph $G$, let $c_2(G)$ denote its $c_2$ invariant. Curves in the geometry associated with $c_2(G)$ correspond to weight-2 modular forms. Cu…

Semilinear reducibility conjecture. For every $h\geq 3$, the graph $\widehat{ZZ}_h$ is semilinearly reducible and, for every $q$ with no primes of bad reduction,

Zigzag completion conjecture. For every $h\geq 3$, the completion $\widehat{ZZ}_h$ is semilinearly reducible and, for every $q$ with no primes of bad reduction,

Completion conjecture. If

Minimal-rank conjecture. For any quantum field theory with enough primitive Feynman graphs, the minimal rank of the gradation is the number of interactions of the theory.

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…