6 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 $(I_i)\in\{0,1\}^k$ 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 $k\geq 2$, let $a_1,\dots,a_k$ be elements for which the displayed multiple polylogarithms are defined, and let $\mathcal{L}_{2k}$ be the weight-$2k$ component of the Lie coalg…

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…

Let $D_{n,k}$ denote the number of multiple zeta values of weight $n$ and depth $k$ that are not reducible to multiple zeta values of lesser depth. Broadhurst–Kreimer conjecture. T…