7 problems

Let $M$ be a manifold with first Chern class $c_1(M)=0$, and let $D$ be the algebra of polydifferential operators on $M$. A BV$_\infty$-structure conjecture asserts that $D$ admits…

BV-infinity lifting conjecture. The map $\mathrm{HKR}$ should lift to a $BV_\infty$ map.

Cao–Zhou conjecture. The BV-algebras

Let $Q$ be a manifold, let $W$ be a Liouville domain of dimension $2n$, and let $\widehat{\mathbb{H}}_*\Lambda$, $\overline{\mathbb{H}}_*\Lambda$, $S\mathbb{H}_*({\partial}W)$, and…

Let $M$ be a simply-connected manifold, let $C^*(M)$ denote its differential graded algebra of singular cochains, and let $LM$ be its free loop space. Write $H^{>0}(LM)$ for the po…

Let $A$ be a commutative cochain algebra model for a space $M$, and let $\widetilde{HH}_*(A)[m-1]$ carry the natural BV structure described in the paper. The BV product conjecture.…

Let a Topological Vertex Operator Algebra have homology groups equipped with Lian and Zuckerman's BV-algebra structure. Lian–Zuckerman's conjecture. This BV-algebra structure lifts…