Date & Time: Wednesday, April 09, 2014, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: S. Ramanan, Chennai Mathematical Institute
Title: Quadric Geometry and Vector Bundles on Curves
Abstract: There is a close relationship between pencils of quadrics (particularly in odd-dimensional projective spaces) and hyper-elliptic curves. Classically, it is known that pencils in P3 give all elliptic curves. Hyper-elliptic curve of genus g as well as their Jacobians can be geometrically described in terms of a pencil in P2g + 1. The moduli of vector bundles of rank 2 on them can also be described in a similar fashion.
Hitchin gave a map of the cotangent bundle of these moduli spaces (which is an open dense subset of the Higgs moduli) into an affine space and one can describe this also geometrically. I shall try and illustrate this in the particular case g = 2.