Cohomology of braids, graph complexes, and configuration space integrals

In this talk, I will explain how three integration techniques for producing cohomology — Chen integrals for loop spaces, Bott-Taubes integrals for knots and links, and Kontsevich integrals for configuration spaces — come together in the computation of the cohomology of spaces of braids.  The relationship between various integrals is encoded by certain graph complexes.  I will also talk about the generalizations to other spaces of maps into configuration spaces (of which braids are an example), and this will lead to connections to spaces of link maps and, from there, to manifold caclulus of functors.  This is joint work with Rafal Komendarczyk and Robin Koytcheff.