Mathematics (MA): Recent submissions
Now showing items 81-100 of 253
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Spectral approximations
The problem of determining the nonzero eigenvalues, if any exist, of a linear operator on a Hilbert space, is a very important one in mathematics and physics. Even when the space is finite-dimensional, the actual ... -
Contractivity, Complete Contractivity and Curvature Inequalities
Let ???A\| \cdot \|_A???A? be a norm on Cm\mathbb{C}^mCm given by the formula ?(z1,…,zm)?A=?z1A1+?+zmAm?\|(z_1, \ldots, z_m)\|_A = \|z_1 A_1 + \cdots + z_m A_m\|?(z1?,…,zm?)?A?=?z1?A1?+?+zm?Am?? for some choice of an ... -
Computation of Lyapunov spectrum and dynamic moment invariants
This thesis consists of two parts. The first part describes a new method of computing the Lyapunov exponents of continuous and discrete dynamical systems. Chaos is observed in a large class of systems and hence the problem ... -
Projective Modules and the Quillen Suslin Theorem
The notion of a module over a ring is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules ... -
Curves on Surfaces
This project report concerns the study of simple closed curves on surfaces. Specifically, we consider the question of when a closed curves on a torus can be deformed to a simple closed curve. We also consider applications ... -
Numerical Techniques for reconstruction of objects from projections
In this dissertation we consider certain alternative procedures, viz., the g-inverse method as well as an iterative technique based on probabilistic estimation for the reconstruction of objects from their projections. ... -
Herglotz representation, approximation by inner functions, and Hankel operators
This thesis can be broadly categorized under the theories of multi-variable operators and holomorphic functions, structured into two distinct parts. The first part investigates the relationship between two classical theorems: ... -
Mapping class group dynamics, relative character varieties and hyperbolic cone surfaces
This thesis concerns the punctured surface group representations into $\pslr$ and $\pslc$. We study the action of mapping class group on the relative character varieties of punctured surface groups into $\pslr$ and $\pslc$. ... -
Some results on beta ensembles and on scaling limits of random graphs
This thesis is divided into two main parts, each of which can be studied independently of the other. The first part is devoted to the study of beta ensembles (β-ensembles). The main theme in β-ensembles, in this thesis, ... -
Positivity properties of the deformed Hermitian-Yang--Mills and related equations
In the first part of the talk, we briefly introduce the deformed Hermitian-Yang-Mills (dHYM) equation and discuss a result regarding the solvability of the twisted dHYM equation on compact Kähler three-folds with slightly ... -
Symmetric real-closed subsets of affine Kac-Moody Lie Algebras
In this thesis, we study some important classification problems related to affine Kac--Moody Lie algebras. First, we address the combinatorial problem of classifying symmetric real-closed subsets of affine root systems ... -
The Momentum Construction Method for Higher Extremal Kähler and Conical Higher cscK Metrics
This thesis consists of two parts. In both the parts we study two new notions of canonical K\"ahler metrics on compact K\"ahler manifolds which were introduced by Pingali, viz. `higher extremal K\"ahler metric' and ... -
Holomorphic mappings and Kobayashi geometry of domains
In this thesis, we study certain aspects of the geometry of the Kobayashi (pseudo)distance and the Kobayashi (pseudo)metric for domains in $\mathbb{C}^n$. We focus on the following themes: on the interaction between Kobayashi ... -
The monopole-dimer model and eccentricities for Cartesian product of graphs
This thesis comprises two main parts. The details of the two parts are as follows: The first part of the thesis deals with the monopole-dimer model. The dimer (resp. monomer-dimer) model deals with weighted enumeration of ... -
Invariants Associated with Complete Nevanlinna-Pick Spaces
The broad aim of this thesis is to study certain tuples of bounded operators that satisfy an operator inequality arising from a complete Nevanlinna-Pick kernel. Specifically, we focus on two invariants of these operator ... -
Maps Between Non-compact Surfaces
This thesis focuses on studying proper maps between two non-compact 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 J-equation} 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 J-flow on the blow-up of the complex projective space at a ... -
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 ... -
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 ...