Jonas Stelzig: Higher operations in complex geometry

Abstract:

In the last decades, several ad hoc definitions of holomorphic higher order operations on complex manifolds have been given, mimicking classical Massey products and their variants. I will explain some context and answer the following two questions: 1) What is the notion of formality which these operations obstruct and 2) Can these operations be nontrivial on compact Kähler manifolds? (Spoiler: Yes!)