**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 *P ^{3}* 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

*P*. The moduli of vector bundles of rank

^{2g + 1}*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*.