Graph-complexes in embedding calculus

Manifold calculus of functors is a machinery invented by Goodwillie and Weiss in order to study spaces of smooth embeddings of one manifold into another. I will briefly recall this construction as well as the connection to operads. For a particular example of the space of long embeddings R^m in R^n, n>2m+1, this connections describes the rational homology and
homotopy as the homology of very explicit graph-complexes similar to those introduced by Kontsevich. As example the non-completed
Grothendieck-Teichmuller Lie algebra always appears as a part of rational homotopy of aforementioned spaces in case of even n.

The talk will be based on a joint work with G. Arone and also on some new joint results with T. Willwacher.