9 problems

Let $\mathfrak{g}^{\mathfrak{m}}$ be the motivic Lie algebra of multiple zeta values, equipped with its depth filtration $D$, and let…

Depth-graded Ihara–Kaneko–Zagier conjecture. All algebraic relations in $\operatorname{gr}_D\mathcal{Z}$ are obtained by comparison of the maps

Let $\mathfrak{bm}_0$ be the Lie algebra candidate defined by the balanced quasi-shuffle primitiveness and $\tau$-invariance conditions, let $\mathfrak{lq}$ be the ambient Lie alge…

Let $\mathcal{A}$ be the quotient of the motivic multiple-zeta-value algebra by $\zeta^{\mathfrak{m}}(2)$, and let the complex constructed by Brown in the cited work be the depth-g…

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