14 problems

Deligne–Drinfeld conjecture. $\mathfrak{grt}_1$ is the completed free Lie algebra with generators $\sigma_3,\sigma_5,\sigma_7,\dots$ of homogeneous weights $3,5,7,\dots$.

Let $\mathfrak{grt}_1$ be the Grothendieck–Teichmüller Lie algebra, and let $\widehat{\operatorname{Lie}}(\sigma_3,\sigma_5,\sigma_7,\ldots)$ denote the free complete Lie algebra o…

Drinfeld's conjecture. The inclusion is surjective; equivalently, $\mathfrak{grt}$ is isomorphic to the free graded Lie algebra with one generator in every odd degree at least $3$.…

Brown's conjecture. The free Lie algebra generated by the $\sigma_{2k+1}$ can be extended to a larger free Lie algebra involving generators of higher degrees as well.

Let $\mathcal{MT}(\mathbb Z)$ be the category of mixed Tate motives over the integers, let $G^{\mathrm{mot}}_{\mathcal{MT}(\mathbb Z)}$ be its motivic Galois group, and let…

Let $\widehat{\mathfrak{krv}}_2$ be the Kashiwara–Vergne Lie algebra, let $\mathfrak{grt}_1$ be the Grothendieck–Teichmüller Lie algebra, and let $\mathfrak{t}_2$ be the two-strand…

For the trivial group, let $\xi({D}_{\bullet \bullet})$ be the image of the dihedral Lie algebra under the displayed embedding, and let ${\cal G}rt_1$ denote the Grothendieck–Teich…

Motivic Grothendieck–Teichmüller criterion. The inclusion

Torsor conjecture. The set of homotopy classes of such morphisms is a torsor over the Grothendieck–Teichmüller group $GRT$. The conjecture predicts that the explicit transcendental…

Multiple-zeta-value quotient conjecture. There is an isomorphism

Deformation-map isomorphism conjecture. The map $\varphi_{\nu}$ is an isomorphism.

Let $X$ be an algebraic variety, and let $H^{\bullet}(X, \mathcal{T}_{\mathrm{poly}})$ denote the cohomology of its sheaf of polyvector fields. The Grothendieck–Teichmüller group…

Let $p>2$ be a prime and let $\mathbb{K}$ be a field of characteristic $p$. Let $A(x,y)$ and $B(x,y)$ be solutions of the partial Kashiwara–Vergne equations, chosen symmetrically s…

Let $\widehat{\operatorname{\mathfrak{kv}}}_2$ be the completed Kashiwara–Vergne Lie algebra, let $\operatorname{\mathfrak{grt}}$ be the Grothendieck–Teichmüller Lie algebra, and l…