Topology and trivalent graphs: Kontsevich invariants

Shruthi Sridhar, Princeton University
Fine Hall 110

Kontsevich defined invariants of knots and 3 manifolds via certain integrals over configuration spaces. They take values in a vector space generated by classes of trivalent graphs.These invariants have been shown to be "universal finite type invariants" for knots (and 3-manifolds). They have also been used to define characteristic class type invariants of fiber bundles. In this talk we will explore some of these fascinating results. Kontsevich was inspired to define these by studying similar invariants coming from perturbative Chern Simons theory, and time permitting, I will describe this analogy.