**Date & Time:** Thursday, January 21, 2016, 15:30-17:30

**Venue:** Room 216

**Title:** Chern-Weil theory

**Speaker: ** Saurav Bhaumik, IIT Bombay

**Abstract:** We will define principal bundles, connections and curvature.
With the basics defined, we will construct the Chern-Weil
homomorphism. Let E be a principal G-bundle on M with a connection D.
Let F be the curvature of D, and g=Lie(G). The Chern-Weil homomorphism
associates to each Ad-invariant polynomial on g, a well defined
cohomology class in the de Rham cohomology H_{dR}^*(M). Let P be an
Ad-invariant homogeneous polynomial of degree k on g. The Chern-Weil
image of P is given by the closed 2k-form P(F^{2k}). Its class in
H^{2k}_{dR}(M) does not depend on the choice of the connection. This
class is functorial. We will conclude with a few examples.