9 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…

The QP-manifold $({\cal M},\omega,Q)$ determines an $L_\infty$-algebra whose brackets have the schematic form … with the brackets antisymmetrised in their arguments. Elements $f_i$…

Let $\mathfrak{g}$ be a vector space considered as a Hom-Lie algebra with the zero Hom-Lie structure, and let…

Let $A$ be an ordinary gauge field with gauge transformations $[\delta_\lambda A$ and let $\hat A(A)$ be its Seiberg–Witten image, with non-commutative gauge transformations…

$L_\infty$-structure conjecture. There is an $L_\infty$-algebra structure on the complex $\mathrm{\tilde{H}\!C}(A)$ such that its Maurer–Cartan elements are precisely the multiplic…

Milnor fiber–Maurer–Cartan conjecture. The homotopy type $MC_{\bullet}(L)$ is equivalent to the homotopy type $\Delta({\mathfrak F}_{x})$.

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…