Ryan Budney (U. of Victoria): Topology of spaces of knots
 
Abstract: 
I will outline what is known about the homotopy-type of spaces of embeddings, 
paying particular attention to operads and their actions on knot spaces, 
the relations with geometrization and finite-type invariants via the Goodwillie-Weiss 
Calculus of Functors.  The most recent developments in this subject involve 
the interaction of operad actions on knot spaces and the "Taylor tower" associated 
to the functor calculus.