33 problems

For a $phi^4$ graph $G$, let $P_G$ denote its Feynman period and let $H_G$ denote its Hepp bound, a combinatorial invariant of $G$. Panzer's Hepp-bound conjecture. Two $phi^4$ grap…

Let $\mathcal{P}_{\phi^3}^{\mathfrak{m}}$ denote the space of motivic periods of six-dimensional $\phi^3$ theory, and let $\mathcal{P}^{\mathfrak{dr}}$ denote the de Rham period sp…

Feynman periods are periods arising from logarithmically divergent subdivergence-free Feynman integrals, and the motivic Galois coaction is expected to extend the Goncharov--Brown…

Brown–Schnetz conjecture. For every prime $p$,

Period--Speyer conjecture. If two cyclically $6$-connected $4$-regular graphs, or two cyclically $4$-connected $3$-regular graphs, satisfy

Let $P_{l,n}$ denote the Feynman period indexed by loop order $l$ and graph number $n$ in the notation of the cited census. Loop-order-eight period conjecture. The first examples o…

Perfect Martin sequence conjecture.

Let $G$ be a cyclically $4$-connected $3$-regular graph with loop number $\ell$ satisfying $7\leq\ell\leq9$, and let $\operatorname{\mathsf{M}}(G^{[4]})$ denote the Martin invarian…

Let $G_1$ and $G_2$ be primitive $\phi^4$ graphs, and let $c_2^{(q)}(G)$ denote the $c_2$-invariant modulo a prime power $q$. Let $\mathcal{P}(G)$ denote the Feynman period. Comple…

Let $G_1$ and $G_2$ be cyclically $6$-connected $4$-regular graphs, and let $v_1$ and $v_2$ be vertices whose deletion produces graphs with periods $\mathcal{P}(G_1\setminus v_1)$…

Let $G$ be a regular graph, and let $\operatorname{\mathsf{M}}(G^{\bullet})$ denote its Martin sequence. For a Feynman graph $G$, let $\mathcal{P}(G)$ denote its Feynman period. Pe…

Let $G_1$ and $G_2$ be primitive divergent graphs, meaning that the completion of each graph is internally 6-edge connected, and let their Feynman periods be defined by the corresp…

Period-determines-extended-graph-permanent conjecture. If $G$ and $H$ have equal periods, then they have equal extended graph permanents.

Period-determines-$c_2$ conjecture. If $G$ and $H$ have equal periods, then they have equal $c_2$ invariants.

Finiteness conjecture. For any fixed dimension, there exist only finitely many $c_2$ invariants among all loop orders.

Let $L_{10}=P_{10,425}$ and let $\mathcal{W}_{12}$ denote the weight-12 component. $L_{10}$ weight decomposition conjecture. The period $L_{10}$ mixes weights $12$ through $14$, an…

For $n\geq3$, let $L_{2n}$ denote the ladder graph period. Ladder weight-mixing conjecture. … This extrapolates from the cases $L_6$ and $L_8$. It is a prediction about the weight…

Let $L_{10}=P_{10,425}$ be the ten-loop ladder period and let $P_{10,1139}$ be the specified ten-loop period. $L_{10}$ exclusion conjecture. … The source motivates this by observin…

Let $G$ be a primitive log-divergent $\phi^4$ graph with loop number $h_G$ and $c_2(G)=-z_3$, and let $\delta_m$ be the derivation with respect to the modified parity basis in the…

Let $\mathcal{Z}_6$ be the source's period space at sixth roots of unity, and let $\mathcal{P}_{\phi^4}$ denote the $\phi^4$ periods. Low-weight real-part conjecture. The only…

Let $G$ be a primitive log-divergent graph with loop number $h_G$ and $c_2(G)=-z_3$. $c_2=-z_3$ conjecture. … The three known examples lie in the indicated space, and the source ob…

Let $G$ be a primitive log-divergent graph with loop number $h_G$ and $c_2(G)=-z_2$. $c_2=-z_2$ conjecture. … Here $\mathcal{Z}_2$ is the algebra of multiple polylogarithmic period…

Let $G$ be a primitive log-divergent $\phi^4$ graph with loop number $h_G$ and $c_2(G)=0$. Suppose $P(G)$ is mixed Tate. Refined weight-mixing conjecture. Either $P(G)$ has pure we…

Let $G$ be a weight-drop graph with loop number $h_G$, and suppose its period belongs to $\mathcal{Z}_N$ for some $N$. Weight-drop bound conjecture. … This is an expected upper bou…

Let $G$ be a primitive log-divergent graph with loop number $h_G$ and $c_2$-invariant $-1$. $c_2=-1$ MZV conjecture. Its period is a multiple zeta value of weight $2h_G-3$: … The p…