7 problems

Let $\mathfrak{d}\mathfrak{g}_1$ be the depth-one part of the depth-graded motivic Lie algebra, let $\mathcal{U}\mathfrak{g}$ be its enveloping algebra, and let $\gamma$ be the nat…

Let $\mathfrak{d}\mathfrak{g}_1$ be the depth-one part of the depth-graded motivic Lie algebra, let $\mathcal{U}\mathfrak{g}$ be its enveloping algebra, and let…

Let $\mathcal{A}=\mathcal{H}/(\zeta^{\mathfrak{m}}(2))$, with depth-graded pieces $gr_r^{\mathfrak{D}}\mathcal{A}$, and let $\mathbb{P}^{\vee}$ be the weight-dual of the restricted…

For each $r\geq 3$, let $gr_r^{\mathfrak{D}}\mathcal{A}^{odd}$ denote the depth-graded totally odd part modulo $\zeta^{\mathfrak{m}}(2)$, let $\mathbb{P}^{\vee}$ be the weight-dual…

Broadhurst–Kreimer–Brown conjecture. The generating series satisfies

Broadhurst–Kreimer's conjecture. The generating series of the dimensions of the weight- and depth-graded parts is

Motivic Broadhurst–Kreimer conjecture. The depth-and-weight generating series satisfies