10 problems

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…

Let ${\rm Gal}_{\rm mot}(\overline{\mathbb Q}/\mathbb Q)$ be Deligne's motivic group, and let $\pi_1^{\rm un}({\mathbb P}^1-\{0,1,\infty\})$ denote the unipotent motivic fundamenta…

Goncharov's conjecture. The Lie algebra $\mathfrak g$ is a prounipotent Lie algebra freely generated by elements $z_3,z_5,z_7,\dots$, where $z_m$ has weight $-2m$.

Comodule conjecture. Primitive Feynman integrals are conjectured to form a comodule under the motivic Galois coaction.

Let $G$ be a primitive log-divergent Feynman graph in $\phi^4$ theory, and let its associated Feynman amplitude be regarded as a motivic period. The motivic Galois group acts on mo…

Let $M_{0,4}$ be the moduli space of four marked points on the projective line, and let its unipotent fundamental groupoid be equipped with its automorphism group. The Deligne–Ihar…

Zagier's conjecture. All relations between multiple zeta values should be implied by double shuffle relations, suggesting

Pollack's conjecture. Any such zeta element $sigma_{2n+1}$ can be expressed as a Lie bracket of the $psi$'s.

Let $GRT_1$ be the Grothendieck–Teichmüller group and let $DMR_0$ be the double shuffle group. Let $G^{\mathrm{mot}}_{\mathbb{Z}}$ denote the motivic Galois group of $\mathbb{Z}$,…