Indian Women and Mathematics

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