20 problems

A graph's completion is the graph obtained by the completion operation referred to in the source, and $c_2$ denotes the $c_2$-invariant of a connected graph with at least three ver…

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

Perfect Martin sequence conjecture.

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

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.

Panzer's Hepp-period identity conjecture. Equality of Feynman periods is equivalent to equality of Hepp periods:

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…

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 $G$ 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 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…

Let $G$ be a primitive log-divergent $\phi^4$ graph with loop number $h_G$ and completion $\overline{G}$, and suppose $P(G)\in\mathcal{Z}_N[\xi_N]$ for some $N$. Let…

Let $G$ be a connected graph with at least three vertices, let $P(G)$ denote its period, and let $c_2(G)$ denote its $c_2$-invariant. Period-$c_2$ invariance conjecture. For two pr…

Let $\mathcal{P}_{\phi^4}$ denote the space of $\phi^4$ periods and let $\zeta(2)$ be the Riemann zeta value at $2$. Non-occurrence conjecture. … No $\phi^4$ graph is known to eval…

Maximum-weight cell-zeta conjecture.

Single-valued period conjecture. The period of any two-dimensional completed primitive graph belongs to