# Higher Homotopy Algebras in Topology @ Max Planck Institute for Mathematics (MPIM Bonn)

## Abstract

Koszul duality is a powerful tool that can be used to produce resolutions of algebras in many contexts. In particular, Koszul duality of operads is the tool of choice to define the notion of homotopy algebras.

In this talk, I will present a framework to study curved Koszul duality for algebras over certain kinds of unital operads (i.e. satisfying $P(0)=k$). I will explain how to use it in order to compute the factorization homology of a closed manifold with values in the algebra of polynomial functions on a standard shifted symplectic space.