University of Toronto's Symplectic Geometry Seminar

Abstract: The classical Chern-Weil theory of characteristic classes associates to every principal bundle over a space B a homomorphism from the ring of invariant polynomials into the cohomology ring of B. It was observed by Cartan that the Chern-Weil construction admits a very nice algebraic reformulation, entering his model for the equivariant cohomology of a space. In this talk I will review the Chern-Weil-Cartan theory, and show how to apply these ideas in the context of Lie algebras. Specifically, one obtains a new interpretation of Duflo's theorem for the special case of quadratic Lie algebras.