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 Geetha Thangavelu: Title: Cellular Algebras Abstract: Cellular algebras were introduced by Graham and Lehrer in 1996. One of 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. 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. 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) Abstract: We will discuss mathematical models in three main streams of management: Marketing, Rukmini Dey: (Subject: Geometry) Title: Minimal Surfaces Abstract: I will introduce minimal surfaces which are surfaces whose mean Shantha Bhushan: (Subject: Topology and Biology) Preeti Raman: (Subject: Number theory) Title: Hasse principle for algebraic groupsClare 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 |