Seminar

I will review the moduli space of rank 2 parabolic bundles on P^1. I will calculate the "very stable" part of this moduli space in the case of 4 parabolic points.

To a local system of complex vector spaces on a topological space Chern and Simons associated natural characteristic classes living in odd-degree cohomology of the space with coefficients in C/Z. These classes refine the Chern classes of the complex vector bundle corresponding to the local system; the latter are always torsion, but Chern-Simons classes are generally non-trivial even rationally. For example, when evaluated on the uniformizing local system of a compact hyperbolic 3-manifold they recover the volume of the manifold.

In this talk aimed at graduate students, I will give a brief overview of the theory of quadratic forms over a field. I will introduce some beautiful related objects, including the Witt ring and Milnor K-theory, and conclude by stating the Bloch-Kato conjecture.