January 8-9-10, 2012 at IMSc, Chennai
Rama Mishra:
Title: Polynomials in Knot theory Talk file
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 Talk file
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.
Preena Samuel:
Title: RSK bases in invariant theory. Talk file
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 Talk file
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. Talk file
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 Talk file
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
Talk file
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
Talk file
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: Talk file
The video of the Chladni experiment was taken from Youtube :
http://www.youtube.com/watch?v=Qf0t4qIVWF4>
and the simulations of Fourier series were taken from this website :
http://www.falstad.com/mathphysics.html
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.
PANEL DISCUSSIONS:
Title: INDIAN WOMEN and MATHEMATICS
2.30 pm -4.30 pm, 9 January
Members:
Ajit Iqbal Singh (Indian Statistical Institute, Delhi)
Talk file
Girija Jayaraman (Indian Inst. of Technology, Delhi)
Talk file
R. Sujatha (Tata Inst. of Fundamental Research, Mumbai)
Talk file
Geetha Venkataraman (Ambedkar University, Delhi)
Talk file
B. SriPadmavathi (University of Hyderabad, Hyderabad)
Talk file
Vijaylaxmi Trivedi (Tata Inst. Of Fundamental Research, Mumbai).
Talk file
Title: MATHEMATICS and CORPORATE WORLD
2.30 pm -4.30 pm, 10 January
Members:
Rajeeva Karandikar (Director, Chennai Mathematical Institute, Chennai)
Shubhasis Gangopadhyay (Director, India Development Foundation, Delhi)
Talk file
Sharadha Ramanan (Senior Scientist, R&D,TCS, Chennai).
Talk file