IWMAbstracts


Rama Mishra:

Title: Polynomials in Knot theory

Abstract: 
    Knots are fascinating objects and more interestingly they are stud-
ied mathematically in a subject known as knot theory. In this talk I
will discuss how polynomials play a crucial role in the study of knots,
be it as invariants for classifying knots or as embeddings for representing them in 3-space.


Mahuya Dutta:

Title:  Handlebody decomposition of a manifold
                                 
Abstract:  
A handle of index k and dimension n, by definition, is a manifold with bound-
ary which is diffeomorphic to D^k × D^{n−k} in R^n , where D^k and D^{n−k} denote balls
in Euclidean spaces R^k and R^{n−k} respectively. It can be shown that a compact
n dimensional manifold without boundary can be developed from a ball D^n by
successively attaching to it finitely many handles of dimension n. This is a funda-
mental result in Morse theory. We will explain the result by means of examples.





Girija Jayaraman:

Title:
Agencies Funding Research in Mathematics and Project Proposal
Guidelines


Preena Samuel:

Title:
RSK bases in invariant theory.

Abstract:
Invariant theory comes as an efficient tool in studying orbits of
spaces under group actions. In this talk we shall look at some
classical examples of groups acting on vector spaces and discuss their
orbits. We discuss a framework where this geometric question can be
posed as an algebraic one, thus bringing in classical invariant theory
into the picture. We then pose our main problem of interest, namely
finding the orbits of the action of the general linear group on the
space of matrices by conjugation, into this setting. The history of
this problem will be briefly discussed and finally, the RSK
basis/generators which provide all the information on the orbit
structure for this action will be introduced along with a sketch of the
proof.






Geetha Thangavelu:

Title:  Cellular Algebras

Abstract:  Cellular algebras were introduced by Graham and Lehrer in 1996.  One of
the central problems in the representation theory of finite groups and finite
dimensional algebras is to determine the number of non-isomorphic simple modules.
 But in the real-world, algebras, especially those with the interesting applications
in mathematics and physics, to parametrize the irreducible representations of these
algebras is quite a hard problem.  One of the strengths of the theory of cellular
algebras is that it provides a complete list of absolutely irreducible modules for
the algebra over a field.  In this talk we will discuss cellular algebras and their
applications to algebras in mathematics and physics.

Usha Bhosle:
Title: Quadrics and vector bundles.

Abstract: The notions of pencils of quadrics, hyperelliptic curves, vector
bundles will be introduced. The beautiful correspondence between quadrics
and vector bundles will be explained.


 
Archana Morye:
Title: Vector bundles over real abelian varieties

Abstract: Holomorphic connections play an important role in the theory of complex
vector bundles. But unlike differentiable connection holomorphic
connection may not exist at all. In the case of holomorphic bundles
over a complex abelian variety, the existence of a algebraic connection is
interlinked with the concept of a stability (semi-stability) of a vector
bundle. Moreover it is a class of homogeneous vector bundles.
Holomorphic connections in holomorphic bundles over a complex
abelian variety were studied by Balaji, Biswas, Gomez, Iyer and
Subramanian. In this talk we will give analogues, for real abelian
arieties, of some of their results. The statement of the problem
will be presented in a way accessible to a wide audience. And finally
discuss various equivalent conditions for the presence of real
holomorphic connections in a real holomorphic vector bundle over a
real abelian variety.



Suneeta Varadarajan

Title:

  Found: Yet another point of intersection between Geometry and Physics

Abstract:

 In 2003, a Russian mathematician, Grisha Perelman, published a proof of the Poincare conjecture, then one of the most important open problems in mathematics. Perelman’s amazing and insightful proof used a differential equation that represented a flow through geometries. In this talk, we will describe this work and then discuss a startling connection of this flow to one of the most important open problems  in fundamental physics: how does the geometry of space(time) change in response to the dynamical change of matter in it?


Riddhi Shah:
 
Title: Dynamics of Distal Group Actions

Abstract: An automorphism $T$ of a locally compact group is said to be distal if
the closure of $T$-orbits of any nontrivial element stays
away from the identity. We discuss some properties of distal actions on groups.

Nalini Anantharaman:

Title:  The semiclassical limit for eigenfunctions of the laplacian : a survey.

Abstract: This will be a (non exhaustive) survey talk about the eigenfunctions of
the laplacian in compact domain, in the asymptotic regime where the
eigenvalue goes to infinity. The issue of ``quantum ergodicity'' is to
understand the places where the eigenfunctions can concentrate. I will
also discuss the geometry of nodal lines.







GROUP LEADERS and GROUP DISCUSSIONS:


Ranja Roy:  (Subject: Topology)

Title: Exploring the Euler Characteristic

 

Abstract: Algebraic Topology is a branch of Mathematics that uses algebraic objects, such as numbers, to study geometric objects called Manifolds. The Euler Characteristic is one such number that we associate to a manifold. In this talk we will discuss briefly the classification of closed 2-manifolds based on Euler Characteristic, and explore the importance of this invariant leading to a specific Euler Characteristic formula in the `Asphericalization of  Manifold’



Usha Mohan: (Subject: Mathematical Modelling)

Title: Mathematical Models in Management
Abstract: 
We will discuss mathematical models in three main streams of management: Marketing,
Accounting and Finance. For a marketing study, we study a mathematical model
expressing the relationship between net revenue and variables that affect it. Next,
we present the accounting cycle in a mathematical formal way and finally we discuss
decision making problems in finance.


Rukmini Dey: (Subject: Geometry)

Title: Minimal Surfaces

Abstract:

I will introduce minimal surfaces which are surfaces whose mean
curvature =0 with a lot of pictures.
I will explain the Weierstrass-Enneper representation of
minimal surfaces using hodographic coordinates. Then I will explain the
link between minimal surfaces and Born-Infeld solitons. If time permits,
I will explain my on-going work on the interpolation between two real
analytic curves by piecewise minimal surfaces.


Punita Batra: (Subject: Algebra and representation theory)

Title: Lie Algebras

Abstract:

I will discuss basics on Lie Algebras.


Shantha Bhushan: (Subject: Topology and Biology)

Topic : Using knot theory in understanding proteins.

Abstract:

The aim of this talk is to present an introduction and overview to the
application of geometry and topology in understanding protein structure and
specifically *knotting of the backbone*. Various mathematical tools and
techniques have been applied in modeling and solving problems in biology.
We focus on topological tools especially from knot theory that would be
helpful in understanding proteins
.

Preeti Raman: (Subject: Number theory)

Title: Hasse principle for algebraic groups

Abstract:
We will discuss the classical Hasse-Minkowski theorem for
quadratic forms and explain the Hasse
principle for algebraic groups using Galois cohomology.

Clare D'Cruz: (Subject: Algebra)

Title: Euclid's Algorithm

Abstract:
Solving Polynomial equations has been of interest and importance. How do we understand the solution set for these equations ?
Can we extend the ideas of Euclid's method for finding the quotient and remainders, for two given integers, to polynomials.
We will discuss the analogue of Euclid's algorithm for polynomials. If time permits, we will also state its applications.



Sanoli Gun: (Number Theory)

Title: Ramanujan and Transcendence

Abstract: I will discuss some of the contributions of Ramanujan and
their effect on modular transcendence theory.




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