5 problems

Let $G$ be a nilpotent group with complex Mal'cev completion, and let $\operatorname{RF}_G$ denote its residual finiteness growth. Mal'cev-completion invariance conjecture. The fun…

For each $n$, let ${\mathfrak{qtr}}_n$ be the Lie algebra generated by the elements $r_{ij}$, subject to the classical Yang–Baxter relations, and let ${\mathbf{QTr}}_n$ be the grou…

Let ${\mathbf{Tr}}_n$ and ${\mathbf{QTr}}_n$ be the triangular and quasitriangular groups, and let ${\mathfrak{tr}}_n$ and ${\mathfrak{qtr}}_n$ be their corresponding Lie algebras.…

Let $\widehat{\Gamma_n}$ be the prounipotent completion of the pure cactus group $\Gamma_n$, and let…

Let $X$ be a space with basepoint $x$, let $\mathbb{V}$ be a $k$-variation of Hodge structure on $X$ for a field $k\subset\mathbb{R}$, and let $R$ be the Zariski closure of the rep…