11 problems

The graphs defined by Kontsevich form a Feynman PROP $K$, and let $F$ denote the forest PROP introduced above. Freeness conjecture. The PROP $K$ is conjectured to be the free PROP…

Kinetic conjecture. In a leading Feynman diagram, the sum of these phases vanishes for every choice of internal wave numbers, with the cancellation holding for $m=0,\ldots,n$.

Kinetic conjecture. In a leading Feynman diagram, the Kirchhoff rule never forces an identification of the form $\delta(k_j)$ with some wave vector $k_j$. In addition, the sum of t…

The paper considers twelve different topologies contributing to subdivergent diagrams and the occurrence of the zeta value $\zeta(3)$ in their evaluations. Knot-theoretic explanati…

Usual-properties conjecture. Each black vertex is the starting point of exactly two arrows labeled by “$\mathrm{e}$” and “$\mu$”, is the endpoint of exactly two arrows also labeled…

Landau-polytope facet-labeling conjecture. There are $1:1$ correspondences

Consider the Poisson sigma model with boundary conditions imposed through Lagrange multipliers: the boundary values of $X$ are constrained to the Lagrangian submanifolds…

Let $m>2$ and let $S_1,S_2,\dots,S_m$ denote the external labels of the observable $\mathcal O_{S_1,S_2,\dots,S_m}$ and of the correlator…

A Feynman diagram is a diagram in perturbation theory, while a rooted map is a graph embedded on an orientable surface with a distinguished root. Topological equivalence conjecture…

Horn-type hypergeometric functions form a broad class of multivariable hypergeometric functions encompassing the examples discussed in the paper. Horn-type hypergeometric-function…

The model has polynomial dependence on $t$ in the leading logarithmic terms of $L(t)$, $\beta_{\varphi_t}$, and $(\varphi_t)_{\rm ren}$, and the recursion formula implies the same…