Knot invariants from homotopy theory

The embedding calculus of Goodwillie and Weiss is a certain homotopy theoretic technique for studying spaces of embeddings. When applied to the space of knots this method gives a sequence of knot invariants which are conjectured to be universal Vassiliev invariants. This is remarkable since such invariants have been constructed only rationally so far and many questions about possible torsion remain open. In this talk I will present some explicit computations, and outline a proof that these knot invariants are surjective maps. This confirms one half of the universality conjecture and also extends to prove some missing cases of the Goodwillie-Klein connectivity estimates.