A well-studied class of attacks on cryptosystems called "side-channel attacks", stems from the additional access that an adversary can get due to the susceptibility of the hardware on which the cryptosystem (e.g., digital ...

In this thesis we investigate single and multi-player stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we investigate zero-sum games with both ...

Significant advancements in genome sequencing techniques and other high-throughput initiatives have resulted in the availability of complete sequences of genomes of a large number of organisms, which provide an opportunity ...

In the first part of this thesis, we study critical points of random polynomials. We choose two deterministic sequences of complex numbers, whose empirical measures converge to the same probability measure in complex plane. ...

Guidance is defined as the determination of a strategy for following a nominal path in the presence of o-nominal conditions, disturbances and uncertainties, and the strategy employed is called a guidance law. Variants of ...

This thesis is divided into three parts. In the first part we study mixed norm estimates for Riesz transforms associated with various differential operators. First we prove the mixed norm estimates for the Riesz transforms ...

Mathematical theory of partial differential equations (PDEs) is a pretty old classical area with wide range of applications to almost every branch of science and engineering. With the advanced development of functional ...

Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories ...

Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this ...