6 problems

A family of spaces (or, more precisely, Artin stacks) $\mathcal{L}_{0,n}$ should exist, equipped with the following structure. The spaces form a cyclic operad and have “forgetful”…

Let the Courant contact model be the local $L_\infty$-algebra construction associated to the relevant Courant algebroid, and let the cubic model be the constrained-field model intr…

Koszul-dual duality conjecture. The derived linear dual of the dg $\operatorname{CE}_\bullet(\operatorname{\mathfrak g})$-comodule…

Let ${\mathfrak{l}}$ denote the composition structure on the category ${\rm \ker}\,\mathbf{Q}$, where the propagators of open string fields are defined from the Poisson-type sigma m…

Kontsevich's cyclic formality conjecture. For each volume form $\Omega\in\Omega^d(M)$ there exists an $L_\infty$-quasi-isomorphism of $L_\infty$-algebras

Tsygan's cyclic formality conjecture. There exists a natural $\mathbb C[[u]]$-linear quasi-isomorphism of $L_\infty$-modules