Anna Sopena Gilboy: Pluripotential Operadic Calculus

Abstract.

For complex manifolds, there exists a refined notion of weak equivalence related to both Dolbeault and anti-Dolbeault cohomology. This class of weak equivalences naturally defines a stronger formality notion. In particular, satisfying the \(\partial \overline{\partial}\)-Lemma property does not imply formality in this new sense. The goal of this talk is to introduce a novel operadic framework designed to understand this homotopical situation. Namely, I will present pluripotential \(A_\infty\) algebras as well as a homotopy transfer theorem based on this strong notion of weak equivalence.