Browsing Mathematics (MA) by Title
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Matchings Between Point Processes
(20140620) 
Mechanising knot Theory
(20180131)Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories ... 
Minimal Crystallizations of 3 and 4 Manifolds
(20180611)A simplicial cell complex K is the face poset of a regular CW complex W such that the boundary complex of each cell is isomorphic to the boundary complex of a simplex of same dimension. If a topological space X is homeomorphic ... 
Mixed Norm Estimates in Dunkl Setting and Chaotic Behaviour of Heat Semigroups
(20180103)This thesis is divided into three parts. In the first part we study mixed norm estimates for Riesz transforms associated with various differential operators. First we prove the mixed norm estimates for the Riesz transforms ... 
Multiscale Modelling of HLA Diversity and Its Effect on Cytotoxic Immune Responses in Influenza H1N1 Infection
(20180606)Cytotoxic Tlymphocytes (CTLs) are important components of the adaptive immune system and function by scanning the intracellular environment so as to detect and destroy infected cells. CTL responses play a major role in ... 
A Multiscale Modeling Study of Iron Homeostasis in Mycrobacterium Tuberculosis
(20180510)Mycobacterium tuberculosis (M.tb), the causative agent of tuberculosis (TB), has remained the largest killer among infectious diseases for over a century. The increasing emergence of drug resistant varieties such as the ... 
Near Optimal Nonmalleable Codes and Leakage Resilient Secret Sharing Schemes
A wellstudied class of attacks on cryptosystems called "sidechannel attacks", stems from the additional access that an adversary can get due to the susceptibility of the hardware on which the cryptosystem (e.g., digital ... 
Nodal sets of random functions
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 ... 
Normal Spectrum of a Subnormal Operator
(20180321)Let H be a separable Hilbert space over the complex field. The class S := {NM : N is normal on H and M is an invariant subspace for Ng of subnormal operators. This notion was introduced by Halmos. The minimal normal ... 
Novel Upwind and Central Schemes for Various Hyperbolic Systems
(20180521)The class of hyperbolic conservation laws model the phenomena of nonlinear wave propagation, including the presence and propagation of discontinuities and expansion waves. Such nonlinear systems can generate discontinuities ... 
Numerical Methods for Elliptic Variational Inequalities in Higher Dimensions
The main emphasis of this thesis is on developing and implementing linear and quadratic finite element methods for 3dimensional (3D) elliptic obstacle problems. The study consists of a priori and a posteriori error ... 
Numerical Simulation Of Converging Nonlinear Wavefronts
(20130124) 
Numerical Study Of Regularization Methods For Elliptic Cauchy Problems
(20110630)Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic ... 
On an ODE Associated to the Ricci Flow
(20180418)We discuss two topics in this talk. First we study compact Ricciflat four dimensional manifolds without boundary and obtain point wise restrictions on curvature( not involving global quantities such as volume and diameter) ... 
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 ... 
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 Critical Points of Random Polynomials and Spectrum of Certain Products of Random Matrices
(20180730)In the first part of this thesis, we study critical points of random polynomials. We choose two deterministic sequences of complex numbers, whose empirical measures converge to the same probability measure in complex plane. ... 
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 ... 
On The Analytic Theory Of Explosions
(20120531) 
On the Geometry and Operator Theory of the Bidisc and the Symmetrized Bidisc
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 nonhomogeneous ...