11 problems

Let $d=d_2+d_k$ be a codifferential, and let $d_e=d_2+d_k+d_l+\cdots$ and $d_e'=d_2+d_k+d_l'+\cdots$ be extensions. Two codifferentials are formally equivalent when a formal automo…

In the BV formalism, let $I$ be a local interaction for a UV-finite theory, and let $r\to 0$ denote the removal of the regularization. Write $l_n^\hbar$ for the multilinear operati…

Let $(F,Q,(-,-),W)$ be a free BV field theory, and suppose its Green's witness $W$ is obtained by truncating an $L_{\infty}$ algebra to its underlying cochain complex. Green-witnes…

$L_{\infty}$-algebra conjecture. There exists an $L_{\infty}$ structure on the complex $({\bf F}^{\bullet}_{{\bf b}^-},\mathcal{Q})$, such that its bilinear operation is the symmet…

Functoriality conjecture. There is an $L_\infty$ morphism from the $L_\infty$ algebra $((\mathcal{A}^+)^{\operatorname{comm}},\{\ell_k^+\})$ of $\Lambda^+$ to the $L_\infty$ algebr…

Assume $\Bbbk$ has characteristic zero and Hypothesis … can be taken to be $\widetilde{SC}_{\Lambda}=SC_{\Lambda}$ with differential $\partial=\ell^1_\beta$. This would eliminate t…

Let $F\colon\mathcal A\to\mathcal B$ be a homological epimorphism of $A_\infty$-algebras, and let $\widetilde{\mathcal A}$ be an $E_n$-algebra enhancing $A$. The $E_n$-enhancement…

Let $A$ be an $A_\infty$ algebra over a characteristic-zero field with a cocommutative, conilpotent coproduct $\Delta$ that is a strict $A_\infty$ morphism … Let $\overline\Delta$…

Let $L$ be an $L_\infty$ algebra. Write $\mathcal C(L)$ for its Chevalley–Eilenberg coalgebra, $\mathcal U L$ for Lada and Markl's universal enveloping $A_\infty$ algebra, and…

Joyce–Song formula. The following identities should hold:

Canonical $L_{\infty}$ morphism conjecture. There is a canonical $L_{\infty}$ morphism from $\Omega^{\bullet}_{\mathbb J,H}$ to the total complex of, extending the given quasi-isom…