5 problems

Goncharov's isomorphism conjecture. The map $\nu_{\bullet,\bullet}^{\cal M}(\mu_N)$ is an isomorphism for either $N=1$, or $N=p$ is a prime and $w=m$.

Let ${\cal C}(G)$ be the refined dihedral Lie coalgebra for a finite commutative group $G$, let ${C}_{\bullet}(G)$ be its graded dual, and let ${\rm Gr}^W{\cal G}^{(l)}$ be the wei…

Let $F$ be an infinite field. The truncated cobracket … is obtained by omitting the $\mathcal{L}_1(F)\wedge\mathcal{L}_{n-1}(F)$ component of the cobracket. Goncharov's classical p…

Let $\mathbb L(F)$ be the Lie coalgebra of multiple polylogarithms over a field $F$, with cobracket $\delta$, and let $\mathbb L^{\operatorname{symb}}(\mathbb C)$ be its symbolic v…

Let ${\cal D}_{\bullet,\bullet}(N)$ be the bigraded dihedral Lie coalgebra associated with $N$-th roots of unity, and let ${\cal C}_{\bullet,\bullet}(N)$ be the depth-graded cyclot…