Title: Polynomially Complete Algebras and its Applications

Abstract: An algebra $A$ with a system of operations $F$ is polynomially complete if any operation on $A$ is a composition of the system $F$ with fixed values of some variables. In the talk we will discuss the basic results of the theory of these algebras and their applications to coding theory.

Title: Computational Number theoretic problems in Cryptography

Abstract:Cryptography and cryptanalysis demand computationally hard problems. We present the notions of computational hardness in these contexts. Two important number theoretic problems of great concern in cryptanalysis are (i) integer factoring and (ii) discrete logarithms. We outline the status of these problems, their relationship to certain other problems and outline some of our work on the number field sieve (NFS). The best heuristics for these problems are sub-exponential in the size of the input. The number field sieve, utilizes the mathematics and algorithms of number fields and linear algebra. We show how large-scale computations of NFS are organized.

Profile of Prof. Ram N. Mohapatra

Click here to View My CV

Click here to View My Website

Title: Applications of Compressive Sensing To Surveillance Problems

Abstract: In many surveillance scenarios, one concern that one faces is how to construct an imager that is capable of capturing a scene with high fidelity and yet not computationally expensive. This could be problematic for two reasons: firstly, the optics and electronics in the camera may have difficulty in dealing with so much information; secondly, information from the imager often needs to be transmitted to a user. Because of bandwidth constraints, this task is non-trivial. In this talk, we shall discuss a mathematical framework that is capable of addressing the two aforementioned issues. This framework is rooted in a technique commonly referred to as "compressive sensing". In this talk, we will consider two of the seminal papers in compressive sensing and will present the key theorems and definitions from the two works. We will then survey three different surveillance scenarios and their respective compressive sensing solutions. The contribution of this work to the field is the development of a distributed compressive sensing model.

Profile of Prof. R. Balasubramanian

Click here to View My CV

Click here to View My Publications

Title: Elliptic Curve in Cryptography

Abstract: In this talk we will introduce to Elliptic Curve Cryp­tography(ECC). We will begin with definition of Elliptic curve some basic goals and ideas of cryptography and how Elliptic curve can be useful and implemented here. We will then discuss the discrete logarithm problem for elliptic curves. We will also discuss some attacks on ECC. We will finish the talk with some celebrated and well known results in this field.

Title: Advancement in Financial Optimization

Abstract: This talk will present some recent progress in financial optimization, especially some recent advancement in cardinality constrained and probabilistically constrained portfolio selection.

Title: CIRCULAR SYMMETRIZATION, SUBORDINATION AND ARCLENGTH PROBLEMS ON CONVEX FUNCTIONS

Title: Statistical Convergence of Order and Some Generalizations