Date: 4 April 2014, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: David L. Johnson, Lehigh University
   Title: Secondary Characteristic Classes and Applications

Abstract.  

Secondary characteristic classes are geometric invariants, constructed
as primitives (antiderivatives) of lifts of primary characteristic forms
to an appropriate space, and give invariants either when the primary
characteristic form vanishes completely, or as a difference form between
two geometric structures. The first appearance of secondary
characteristic classes was Chern's proof of the generalized Gauss-Bonnet
theorem, but was used by him only in a limited way.

A beautiful paper by Chern and James Simons in 1974 re-constructed
Chern's original transgressive forms in a more general setting, and
initiated the study of these secondary invariants in their own
right. The first non-trivial such invariant was constructed on a compact
3-manifold as a conformal invariant, but has become a fundamental
"action integral" in theoretical physics.

I will discuss further applications of these invariants, too:
* Moduli problems for vector bundles (Jacobians)
* Boundary terms for characteristic classes
* Ricci flow