Mathematics (MA)
Recent Submissions

Geometry of normed linear spaces in light of BirkhoffJames orthogonality
In this thesis, we have tried to understand the geometry of normed spaces in the light of BirkhoffJames orthogonality. Using the first two chapters to give introductory notes and to establish relevant notations and ... 
Some Aspects of Weighted Kernel Functions on Planar Domains
The broad aim of this thesis is to study some aspects of weighted kernel functions. In particular, this thesis has been driven by three principal goals: First, to study the boundary behaviour of weighted Bergman kernels. ... 
Characters of classical groups twisted by roots of unity
This thesis focuses on the study of specialized characters of irreducible polynomial representations of the complex classical Lie groups of types A, B, C and D. We study various specializations where the characters are ... 
Harmonic Map Heat Flow and Framed Surfacegroup Representations
This thesis concerns the construction of harmonic maps from certain noncompact surfaces into hyperbolic 3space H3 with prescribed asymptotic behavior and has two parts. The focus of the first part is when the domain ... 
On commuting isometries and commuting isometric semigroups
This thesis consists of two parts commuting isometries and commuting isometric semigroups. In the first part, we study the Taylor joint spectrum for a pair of commuting isometries in certain cases. We show that the joint ... 
On some canonical metrics on holomorphic vector bundles over Kahler manifolds
This thesis consists of two parts. In the first part, we introduce coupled Kähler Einstein and HermitianYangMills equations. It is shown that these equations have an interpretation in terms of a moment map. We identify ... 
Interaction of distinguished varieties and the NevanlinnaPick interpolation problem in some domains
This thesis explores the interplay between complex geometry and operator theory, focusing on characterizing certain objects from algebraic geometry. Two concepts that have been of prime importance in recent times in the ... 
Correlations in multispecies asymmetric exclusion processes
The main aim of this thesis is to study the correlations in multispecies exclusion processes inspired by the research of Ayyer and Linusson (Trans. AMS., 2017) where they studied correlations in the multispecies TASEP on ... 
Homogenization of PDEs on oscillating boundary domains with L1 data and optimal control problems
This thesis comprehensively studies the homogenization of partial differential equations (PDEs) and optimal control problems with oscillating coefficients in oscillating domains. After the introduction, the thesis is divided ... 
Local Projection Stabilization Methods for the Oseen Problem
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 ... 
Learning Filters, Filterbanks, Wavelets and Multiscale Representations
The problem of filter design is ubiquitous. Frequency selective filters are used in speech/audio processing, image analysis, convolutional neural networks for tasks such as denoising, deblurring/deconvolution, enhancement, ... 
Weights of highest weight modules over KacMoody algebras
In this dissertation, broadly, we treat the weightsets of arbitrary highest weight modules (uniformly) over all general complex KacMoody Lie algebras $\mathfrak{g}$, achieving the below. We obtain a uniform, explicit, ... 
Quasianalytic Functions, Spherical Means, and Uncertainty Principles on Heisenberg Groups and Symmetric Spaces
This thesis has two parts. The first part revolves around certain theorems related to an uncertainty principle and quasianalyticity. In contrast, the second part reflects a different mathematical theme, focusing on the ... 
Hardy's inequalities for Grushin operator and Hermite multipliers on Modulation spaces
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 ... 
Homogenization of certain PDEs and associated optimal control problems on various rough domains
This thesis is devoted to the study of the asymptotic behavior of partial differential equations (PDEs) and associated boundary and interior optimal control problems in various oscillatory domains. The present thesis ... 
Finite Element Analysis of Optimal Control Problems Governed by Certain PDEs
The primary goal of this thesis is to study finite element based \textit{a priori} and \textit{a posteriori} error analysis of optimal control problems of various kinds governed by linear elliptic PDEs of second order. ... 
Positivity preservers forbidden to operate on diagonal blocks
The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., ... 
On certain invariant measures for correspondences, their analysis, and an application to recurrence
The aim of this dissertation is to analyse a certain class of dynamically interesting mea sures arising in holomorphic dynamics that goes beyond the classical framework of maps. We study measures associated with semigroups ... 
Hermitian Metrics and Singular Riemann Surface Foliations
The main aim of this thesis is to understand curvature properties of a given hermitian metric by restricting it to the leaves of a suitable singular Riemann surface foliation. We will specifically consider the complete ...