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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 ...
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 Bargmann-Fock spaces on the complex ...
On regular subalgebras of symmetrizable Kac-Moody algebras and related combinatorics
In this thesis, we study two aspects of Kac-Moody algebras. One is to understand the subalgebras that can be embedded inside a Kac-Moody algebra as subalgebras generated by real root vectors. The other one is to explicitly ...
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 J-flow
on the blow-up of the complex projective space at a ...
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. ...
Dominating surface-group representations via Fock-Goncharov coordinates
Pls see Abstract pdf file
Geometry of normed linear spaces in light of Birkhoff-James orthogonality
In this thesis, we have tried to understand the geometry of normed spaces in the light of Birkhoff-James orthogonality. Using the first two chapters to give introductory notes and to establish relevant notations and ...
Interaction of distinguished varieties and the Nevanlinna-Pick 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 ...