7 problems

Let $m,n$ be positive integers, let $\xi^m_n$ denote the generator indexed by $m$ inputs and $n$ outputs, and let $\partial$ be the perturbed differential in the minimal model of t…

Transitivity conjecture. The element $\mathbf R^{(\boldsymbol{\epsilon})}$ solves the QYBE. This is expected to provide a large noncommutative class of QYBE solutions analogous to…

Let $G,G',H,H'$ be compact Lie monoids, let $X,X'$ be closed smooth manifolds acted on by $G\times H$ and $G'\times H'$ respectively, let $\varphi\colon G\to G'$ and…

Fix $\alpha\geq1$, and let $\mathcal{A}_{\Pi_{(A_{2},\alpha)}}$ be the graded algebra associated with the preprojective construction for the quiver of type $A_{2}$ with multiplicit…

Let $A$ be a primitive bialgebra in a braided monoidal abelian category, and let ${\mathbb{B}\mathbb{B}}_n(A)$ denote its $n$th bibar-cube, viewed as a double representation of…

Let $R$ be a unital associative ring and let $\mathrm{GL}(R)$ denote its infinite linear group. Write $\mathrm{HL}_{\bullet}(\mathrm{GL}(R),\Bbbk)$ for the Leibniz homology of this…

Kontsevich's conjecture. The graded algebra $H_{GS}(H,H)$ is a $3$-algebra, that is, an algebra over the homology of the little $3$-cubes operad $\mathcal{C}_3$.