7 problems

Let $L=(G,\circ)$ and $M=(G,*)$ be Moufang loops on the same set $G$ of order $n$, and define their distance by … Suppose that $L$ and $M$ have nonequivalent associators. Distance-…

Let $C$ be a smooth curve, let $\operatorname{Conf}(C,n)$ be the configuration space of $n$ distinct points on $C$, and let $\operatorname{Conf}^f(C,n)$ denote its framed version.…

Let $\mathcal M^{B}_{un}(Ran(\mathbb A^1))$ and $\mathcal M^{dR}_{un}(Ran(\mathbb A^1))$ be the Betti and de Rham categories equipped with their natural tensor structures and fiber…

Product decomposition conjecture. The characteristic function of any multiplicity-free cnu contractive associator in $B_n^*(\mathbb D)$ is the pointwise product of the characterist…

Let $A(M^{\delta}_0)$ be the cooperadic algebra of Brown's compactified moduli spaces, let $\boldsymbol{\mathcal{Z}}_{\scriptstyle{\mathrm{ns}}}(A(M^{\delta}_0))$ be the associated…

Let $A(M^{\delta}_0)$ be the cooperadic algebra of Brown's compactified moduli spaces, let $\boldsymbol{\mathcal{Z}}_{\scriptstyle{\mathrm{ns}}}(A(M^{\delta}_0))$ be the associated…

Transcendence Conjecture. The morphism $\varphi_{KZ}$ is injective. This asserts algebraic independence of the coordinate functions of the associator in the sense encoded by the co…