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 ...

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 ...

Let o be the ring of integers of a non-Archimedean local field such that the residue field has characteristic p: Let p be the maximal ideal of o: For Char¹oº = 0; let e be the ramification index of o: i.e., 2o = pe: Let ...

This thesis is made up of two independent parts. We begin the first part by showing that the collection of all prime ideals of a monoid or, in other words, the spectrum of a commutative monoid, endowed with the Zariski ...

In the first part of the talk we would discuss a topic about the Fourier coefficients of modular forms. Namely, we would focus on the question of distinguishing two modular forms by certain ‘arithmetically interesting’ ...