Mathematics (MA)
Recent Submissions

Invariants Associated with Complete NevanlinnaPick Spaces
The broad aim of this thesis is to study certain tuples of bounded operators that satisfy an operator inequality arising from a complete NevanlinnaPick kernel. Specifically, we focus on two invariants of these operator ... 
Maps Between Noncompact Surfaces
This thesis focuses on studying proper maps between two noncompact surfaces with a particular emphasis on the topological rigidity and the Hopfian property. Topological rigidity is the property that every homotopy equivalence ... 
On two complex Hessian equations and convergence of corresponding flows
This thesis consists of three parts. Two important complex Hessian equations are studied on certain compact K\"ahler manifolds from different perspectives. The first one is the {\em Jequation} introduced independently by ... 
On existence and regularity of some complex Hessian equations on Kahler and transverse Kahler manifolds
The thesis consists of two parts. In the first part of the thesis, we classify the convergence behaviour of rotationally symmetric solutions to the modified Jflow on the blowup of the complex projective space at a ... 
On regular subalgebras of symmetrizable KacMoody algebras and related combinatorics
In this thesis, we study two aspects of KacMoody algebras. One is to understand the subalgebras that can be embedded inside a KacMoody algebra as subalgebras generated by real root vectors. The other one is to explicitly ... 
Existence and implications of positively curved metrics on holomorphic vector bundles
This thesis is divided into two parts. In the first part, we study interpolating and uniformly flat hypersurfaces in complex Euclidean space. The study of interpolation and sampling in the BargmannFock spaces on the complex ... 
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 ...