Rational homotopy type of embedding spaces

I will talk about my joint work with Benoit Fresse and Thomas Willwacher. Using the Goodwillie-Weiss embedding calculus and methods of the rational homotopy theory we construct L-infinity algebras of diagrams that encode the rational type of connected components of spaces of embeddings of manifolds in R^n. This rational type depends on the component. Different known invariants of embeddings are conjectured to be responsible for this type.