Mathematics (MA): Recent submissions
Now showing items 21-40 of 153
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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 ... -
Role of gamma oscillations in processing of natural stimuli
Gamma oscillations (~30-80 Hz) are a prominent signature of electrophysiological signals recorded from the brain with proposed roles in various cognitive functions such as attention and visual perception. Although gamma ... -
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 non-homogeneous ... -
Near Optimal Non-malleable Codes and Leakage Resilient Secret Sharing Schemes
A well-studied class of attacks on cryptosystems called "side-channel 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 ... -
Structural connectivity correlates of human cognition explored with diffusion MRI and tractography
Intact structural connectivity among brain regions is critical to cognition. Structural connectivity forms the substratum for information flow between brain regions, and its plasticity is a hallmark of learning in the ... -
Algorithmic and Hardness Results for Fundamental Fair-Division Problems
The theory of fair division addresses the fundamental problem of dividing a set of resources among the participating agents in a satisfactory or meaningfully fair manner. This thesis examines the key computational challenges ... -
Representations of Special Compact Linear Groups of Order Two : Construction, Representation Growth, Group Algebras and Branching Laws
Let o be the ring of integers of a non-Archimedean local field such that the residue field has characteristic p: Let p be the maximal ideal of o: For Char¹oº = 0; let e be the ramification index of o: i.e., 2o = pe: Let ... -
Some results on Spectral spaces and Spectral sequences
This thesis is made up of two independent parts. We begin the first part by showing that the collection of all prime ideals of a monoid or, in other words, the spectrum of a commutative monoid, endowed with the Zariski ... -
Fourier coeffcients of modular forms and mass of pullbacks of Saito–Kurokawa lifts
In the first part of the talk we would discuss a topic about the Fourier coefficients of modular forms. Namely, we would focus on the question of distinguishing two modular forms by certain ‘arithmetically interesting’ ... -
Characterization of Brain Signals Across Scales Using Temporally Modulated Visual Stimuli
Electrical signals from the brain can be recorded at several different scales, ranging from spiking activity to local field potential (LFP) in animals to scalp electroencephalogram (EEG) in humans. Each signal represents ... -
Correlation Functions in the Finite Toom Model
This thesis is divided into four chapters. In Chapter 1, we give some basic definitions and results that we need throughout the thesis. In Chapter 2, we describe the pn0;n1q-Toom model and prove some known results about ... -
Duality for Spaces of Holomorphic Functions into a Locally Convex Topological Vector Space
Consider an open subset O of the complex plane and a function f : O ÝÑ C. We understand the concept of holomorphicity of a complex-valued function. Suppose a function f defined on O takes values in a locally convex ... -
A Study of Some Conformal Metrics and Invariants on Planar Domains
The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. We will be interested in the invariants associated to the ... -
Decomposition of the tensor product of Hilbert modules via the jet construction and weakly homogeneous operators
Let ½ Cm be a bounded domain and K :£!C be a sesqui-analytic function. We show that if ®,¯ È 0 be such that the functions K® and K¯, defined on £, are non-negative definite kernels, then theMm(C) valued function ... -
Trace Estimate For The Determinant Operator And K- Homogeneous Operators
Let $\boldsymbol T=(T_1, \ldots , T_d)$ be a $d$- tuple of commuting operators on a Hilbert space $\mathcal H$. Assume that $\boldsymbol T$ is hyponormal, that is, $\big [\!\!\big [ \boldsymbol T^*, \boldsymbol T \big ]\!\! ... -
Total variation cutoff for random walks on some finite groups
This thesis studies mixing times for three random walk models. Specifically, these are random walks on the alternating group, the group of signed permutations and the complete monomial group. The details for the models are ... -
On the Kobayashi geometry of domains
In this thesis we study questions broadly related to the Kobayashi (pseudo)distance and (pseudo)metric on domains in ℂn. Specifically, we study the following subjects: Estimates for holomorphic images of subsets in convex ... -
Risk-Sensitive Stochastic Control and Differential Games
This thesis studies risk-sensitive stochastic optimal control and differential game problems. First, we study risk-sensitive stochastic differential games for controlled reflecting diffusion processes in a smooth bounded ... -
Sparse bounds for various spherical maximal functions
Harmonic analysis mainly deals with the qualitative and quantitative properties of functions and transforms of those functions. It has applications in various areas of Mathematics like PDE, Differential geometry, Ergodic ... -
Geometric invariants for a class of submodules of analytic Hilbert modules
Let $\Omega \subseteq \mathbb C^m$ be a bounded connected open set and $\mathcal H \subseteq \mathcal O(\Omega)$ be an analytic Hilbert module, i.e., the Hilbert space $\mathcal H$ possesses a reproducing kernel $K$, the ...