Monday 2nd September:
    3pm: Murali Vemuri, The Brylinski Beta Function.
    4pm: Pabitra Barik, Hitchin pairs on a singular curve.

Tuesday 3rd September:
    3pm: Rohith Varma, Higgs bundles on elliptic surfaces.
    4pm: Clare D'Cruz, Finitely supported ideals.

Wednesday 4th September:
    3pm: Krishna Hanumanthu, Syzygies of some GIT quotients.
    4pm: Rajeeva Karandikar, Introduction to Monte Carlo Simulation.

Thursday 5th September:
    3pm: Purusottam Rath, On Schanuel's conjecture.
    4pm: Pramath Sastry, The Hilbert Scheme of divisors on an Abelian Variety.

Friday 6th September:
    2pm: Dishant Pancholi, h-principle in geometry and topology.
    
Tuesday 10th September:
    3pm: Govind Krishnaswami, Modular forms and Hecke operators: a physical interpretation.
    4pm: Prem Prakash Pandey, An application of annihilators of class groups.

Abstracts:

Pabitra Barik, Hitchin pairs on a singular curve.
Abstract: We present  the moduli problem of rank-2 torsion free Hitchin pairs
of fixed Euler characteristic on a reducible nodal curve. We  describe the
moduli space of the Hitchin pairs. We define the analogue of the classical
Hitchin map and describe the geometry of general Hitchin fibre.


********************************
Clare D'Cruz, Finitely supported ideals.
Abstract: Zariski studies complete ideals in  a two dimensional regular
local ring. In higher dimension one needs to look at finitely supported
ideals. In this talk I will try to generalise a few results to higher
dimension.


********************************
Krishna Hanumanthu, Syzygies of some GIT quotients.
Abstract: Let Y be the GIT quotient of a complex projective variety X by a
reductive algebraic group G. We assume that X and G are defined over the
ring of integers and that the base change of X over any prime number is
Frobenius split.

We study the syzygies of a line bundle on Y that is the descent of an ample
line bundle on X.  Using Frobenius split methods, we prove a cohomology
vanishing theorem on Y and, as a consequence, obtain a general result on
N_p property after applying a criterion of Green and Lazarsfeld. Finally we
give two applications to our main result: the case of a finite group acting
on a projective space and the torus action on Schubert varieties.

This talk is based on joint work with S Senthamarai Kannan.


********************************
Rajeeva Karandikar, Introduction to Monte Carlo Simulation.
Abstract: The talk will be a introduction to the powerful technique known as
Simulation. This is a numerical technique and it helps one get answers for
problems for which closed form solutions are not available.

The applications include problems that may not have anything to do with a
stochastic model, such as numerical integration and is also useful in
various problems involving stochastic models, such as risk assessment of
financial instruments.

I will also discuss some examples of interest, such as assessing impact of
negative marking (or absence thereof) on multiple choice tests.


********************************
Govind Krishnaswami, Modular forms and Hecke operators: a physical interpretation
Abstract: We recall parts of the classical theory of elliptic modular forms
and Hecke's operators on them. The mathematical constructions will be
motivated by physical ideas from gravitation, classical and quantum
mechanics. Following ideas of S. G. Rajeev and our work on hadrons, we
briefly outline some approaches to address the basic problem of Hecke
theory. No special background in physics or number theory is assumed.



********************************
Dishant Pancholi, h-principle in geometry and topology.
Abstract: We will discuss through examples the philosophy of "h-principle" and
its applications in solving under determined partial differential relations
arising from geometry.

********************************
Prem Prakash Pandey, An application of annihilators of class groups.
Abstract: We will describe a set of annihilators for class group of
cyclotomic fields. Then use that to prove a theorem about Catalan's
equation. This was the first of the three theorem due to Mihailescu towards
a proof of the Catalan conjecture.

********************************
Purusottam Rath, On Schanuel's conjecture.
Abstract: One of the central questions in the subject of transcendental
numbers is a conjecture of Schanuel. We shall describe this conjecture and
its various ramifications in relation to some of our ongoing work. Time
permitting, I will indicate some future  possibilities I hope to pursue in
relation to this theme.


********************************
Rohith Varma, Higgs bundles on elliptic surfaces.
Abstract: Consider elliptic surfaces X ---> C, with no multiple fibers and
with euler characteristic of X positive. We then have the pushforward map
between the fundamental groups of X and C is an isomorphism.  Consequently
the space of representations into GL(n,C) of these groups are naturally
homeomorphic. The latter spaces (under further conditions ) can be
interpreted as moduli spaces of higgs bundles with vanishing chern classes
on X and C. Hence in principle we can expect an isomorphism of these moduli
varieties. We will try to do the same for rank 2 higgs bundles.


********************************
Murali Vemuri, The Brylinski Beta Function.
Abstract: An analogue of Brylinski's knot beta function is defined for a
submanifold of d-dimensional Euclidean space. This is a meromorphic
function on the complex plane. The first few residues are computed for a
surface in three dimensional space.  Connections with Willmore theory will
be speculated.