Victor Groth: Commutative Bidifferential Bigraded Algebras and Formality

Abstract: In this talk I will introduce the theory of commutative bidifferential bigraded algebras (cbba's). These are bigraded generalisations of commutative differential graded algebras (CDGAs), which are used in rational homotopy theory to study the rational homotopy type of topological spaces. The definition is motivated by complex differential forms on a complex manifold, and Jonas Stelzig is currently studying them in a new field he calls pluripotential homotopy theory. I will give an algebraic introduction to these objects, assuming no prior knowledge of complex manifolds or rational homotopy theory, and give some motivation for why they are interesting. The talk is based on my master's thesis, which focuses on the notion of formality from rational homotopy theory.