14 problems

Uneven Broadhurst–Kreimer conjecture. The bigraded dimensions of the totally odd part are given by

Kernel conjecture. For every $N\geq 2$,

Let $\xi_B$ and $\xi_D$ be the block-graded and depth-graded functionals associated with the relations in the preceding block-to-depth reduction theorem, and let $\sigma$ be an ele…

Let ${\mathcal{D}}_n$ and ${\mathcal{B}}_{n-1}$ denote the depth and block filtrations, and work modulo products. Lower-depth totally odd spanning conjecture. The vector space … is…

Depth-to-even-block isomorphism conjecture. The map ${\mathfrak{s}}{\mathfrak{d}}{\mathfrak{g}}\to{\mathfrak{e}}{\mathfrak{b}}{\mathfrak{g}}$ is an isomorphism. It is stated to hol…

Totally odd spanning conjecture. Totally odd zeta values of depth $r$ span this vector space. The claim is a reformulation of the proposed identification between the totally odd pa…

Let ${\mathfrak{d}}{\mathfrak{g}}$ be the depth graded motivic Lie algebra, let ${\mathfrak{s}}{\mathfrak{d}}{\mathfrak{g}}$ be the subalgebra generated by the non-exceptional elem…

Let ${\mathfrak{d}}{\mathfrak{g}}$ be the depth graded motivic Lie algebra, and let $\mathrm{S}$ be the space of cusp forms for $\mathrm{SL}_2(\mathbb{Z})$. Homological Broadhurst–…

Broadhurst--Kreimer conjecture. We have

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 $\mathcal{A}=\mathcal{H}/(\zeta^{\mathfrak{m}}(2))$, 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

For positive integers $N$ and $r$, let $C_{N,r}$ and $E_{N,r}$ be the matrices used to encode the linear relations among totally odd multiple zeta values, and let…