8 problems

Let $F$ be the field under consideration, let $k$ be a positive integer, and let $\mathcal{G}_k$ be the quotient of $\operatorname{gr}_k^\mathcal{D}\mathcal{L}_{2k}(F)$ by the subs…

Let $F$ be the field under consideration, let $k$ be a positive integer, and let $x_1,\ldots,x_k$ be arguments for the motivic multiple polylogarithm…

For positive integers $n_1,\dots,n_d$ with weight $n=n_1+\dots+n_d$, let $\operatorname{Li}_{n_1,\dots,n_d}(x_1,\dots,x_d)$ be a multiple polylogarithm of depth $d$. Goncharov–Rude…

Let $F$ be the field under consideration, let $k$ be a positive integer, and let $(I_i)\in\{0,1\}^k$ specify which arguments are specialized to $1$. Let…

Let $F$ be the field under consideration, let $k$ be a positive integer, let $x_2,\ldots,x_k\in F^\times$, and let $w_0,\ldots,w_4\in\mathbb{P}^1(F)$. For each $i$, omit $w_i$ from…

Let $\mathcal{L}(\mathrm{F})$ be the Lie coalgebra filtered by depth, and let $\mathrm{gr}^{\mathcal{D}}_k\mathcal{L}_{2k}(\mathrm{F})$ be its depth-$k$, weight-$2k$ component. Wri…

For integers $k>r\ge3$, let $\mathcal H^{al}_{k,r}$ be the $\mathbb Q$-vector space defined from products of depth-graded motivic multiple zeta values with one even index, and let…

Uneven part of the motivic Broadhurst–Kreimer conjecture.