In this dissertation, broadly, we treat the weight-sets of arbitrary highest weight modules (uniformly) over all general complex Kac-Moody Lie algebras $\mathfrak{g}$, achieving the below. We obtain a uniform, explicit, ...

Finite element approximation of fluid flow problems with dominant convection exhibit spurious oscillations. To eliminate these nonphysical oscillations one needs to incorporate stabilizations that can curb the effect of ...

This thesis consists of two parts. In the first part, we introduce coupled Kähler- Einstein and Hermitian-Yang-Mills equations. It is shown that these equations have an interpretation in terms of a moment map. We identify ...

This thesis has two parts. The first part revolves around certain theorems related to an uncertainty principle and quasi-analyticity. In contrast, the second part reflects a different mathematical theme, focusing on the ...

This thesis consists of two broad themes. First one revolves around the Hardy's inequalities for the fractional power of Grushin operator $\G$ which is chased via two different approaches. In the first approach, we first ...

The theory of fair division addresses the fundamental problem of dividing a set of resources among the participating agents in a satisfactory or meaningfully fair manner. This thesis examines the key computational challenges ...

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 ...

Gamma oscillations (~30-80 Hz) are a prominent signature of electrophysiological signals recorded from the brain with proposed roles in various cognitive functions such as attention and visual perception. Although gamma ...

This work is concerned with the geometric and operator theoretic aspects of the bidisc and the symmetrized bidisc. First we have focused on the geometry of these two do- mains. The symmetrized bidisc, a non-homogeneous ...

This thesis is devoted to the study of nodal sets of random functions. The random functions and the specific aspect of their nodalset that we study fall into two broad categories: nodal component count of Gaussian Laplace ...