Colloquium 2:
Time, Day, Date: 24rd October, Thursday 4:00 pm
Venue ; Ramanujan Hall
Speaker: S. Ramanan
Title : Hyperelliptic curves and Geometry of quadrics
Abstract : There is a deep relationship between hyper-elliptic curves of
genus $g$ and quadric geometry in a projective space of dimension $2g +1$.
When $g = 2$, this was investigated by Klein in the 19th century.
Narasimhan and I related this to the moduli of vector bundles. Usha and I
generalised the results to arbitrary genus. Recently I modified and
formulated the proofs in such a way that it would work over a number
field. This was used by Parimala Raman and Jaya Iyer to get
number-theoretic consequences. I propose to give a summary of my methods
which yield some additional consequences as well.