Prof. K.R. Nagarajan's 80th Birthday Meet
CMI, Monday, December 9, 2013
Programme

12.45–14.00: Lunch

14.00–15.00: Hilbert coefficients of local rings by Krishna Hanumanthu, CMI
Abstract:
Hilbert functions of graded commutative rings are interesting and
important objects of study. They are related to classical
geometric invariants, such as the dimension and degree of a
projective variety. Their study naturally extends to local
rings, where we look at the Hilbert functions of the associated
graded algebras.
We consider a CohenMacaulay local ring and study the Hilbert
functions and coefficients associated to them. There are several
interesting questions on these coefficients, including bounds on
them. We will present some results obtained in a joint work with
Craig Huneke.

15.00–15.15: Tea Break

15.15–16.15: Higgs bundles on Elliptic surfaces by Rohith Varma, CMI
Abstract:
Consider triples (X,C,f) where X is a smooth
projective surface (complex), C is a smooth curve
and f: X → C is a surjective map, whose general
fibers are elliptic curves. It is known that in the case of Euler
characteristic of X positive, we have an isomorphism of
the fundamental group of X and orbifold fundamental
group of C (the orbifold stucture is over the points
where f has multiple fibers). Hence the representation spaces
(into GL_{n}) of the two groups are naturally
isomorphic (as complex analytic spaces). Both these spaces
following the work of Hitchin, Simpson et al can be identified
(topologically) as certain moduli spaces of Higgs bundles
on X and moduli spaces of parabolic bundles
on C. The aim of the talk is to demonstrate an algebraic
geometric correspondence between these moduli spaces under
certain assumptions on X.

16.15–17.00: Felicitations

17.00–17.30: High Tea
