Characteristic forms

"Starting with the notion of Stiefel-Whitney classes, Chern moves on to the case of a complex vector bundle and the definition of a characteristic form. These concepts lead to the definition of the celebrated Chern-Simons forms and a certain global conformal invariant that has proven to be extremely useful in physics."@en
"This DVD captures a lecture by one of the legendary figures of modern mathematics, Shiing S. Chern, who brings a masterly touch and profound intuition to the subject of characteristic forms. Starting with the notion of Stiefel-Whitney classes, he moves on to the case of a complex vector bundle and the definition of a characteristic form. These concepts lead to the definition of the celebrated Chern-Simons forms and a certain global conformal invariant that has proven to be extremely useful in physics. Chern also discusses the related $\eta$-invariant of Atiyah, Patodi, and Singer. Touching on the uses of these kinds of ideas in quantum field theory and other areas of physics, Chern makes some predictions about fruitful directions for future research in geometry. The lecture would be accessible to advanced undergraduates and graduate students having a good grasp of the fundamentals of differential geometry and algebraic topology."