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Quasi-analytic 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 quasi-analyticity. In contrast, the second part reflects a different mathematical theme, focusing on the ...
Weights of highest weight modules over Kac-Moody algebras
In this dissertation, broadly, we treat the weight-sets of arbitrary highest weight modules (uniformly) over all general complex Kac-Moody Lie algebras $\mathfrak{g}$,
achieving the below.
We obtain a uniform, explicit, ...
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’ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...