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THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS
(2019-05-10)
Even though the problem of counting points with integer coordinates on a (rational) polytope has connections to sophisticated mathematical topics like Algebraic K-Theory, Fourier-Dedekind Sums, Heegard-Floer Homology, ...
ELLIPTIC CURVES AND PARAMODULAR FORMS
(2019-08-01)
There is a lifting from a non-CM elliptic curve $E/\mathbb{Q}$ to a cuspidal paramodular newform $f$ of degree $2$ and weight $3$ given by the symmetric cube map. We find a description of the level of $f$ in terms of the ...
Dynamics and Stability of Buoyancy-Induced Flows
(2019-05-10)
The present dissertation tackles two different problems in fluid mechanics. In the first problem, we study the stability of free or natural convection of a compressible fluid over a heated plate underlying a semi-infinite ...
GEOMETRIC QUANTIZATION OF A SEMI-GLOBAL MODEL OF A FOCUS-FOCUS SINGULARITY
(2019-08-01)
Quantization of a classical mechanical system is an old problem in physics.
In classical mechanics, the evolution of the system is given by a Hamiltonian vector field
on a symplectic manifold (``phase space''). ...
Representations of the Automorphism Group of a Right-Angled Coxeter Group
(2019-05-10)
In 2009 Grunewald and Lubotzky published a paper in which they defined a family of linear representations of the automorphism group of a free group. In this dissertation, we will use their ideas to construct a family of ...
MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA
(2019-08-01)
Muto, Narita and Pitale construct counterexamples to the Generalized Ramanujan Conjecture for GL(2,B) over the division quaternion algebra B with discriminant two via a lift from SL(2). In this dissertation, I characterize ...
Cubulating one-relator products with torsion
(2019-05-10)
Since the resolution of the virtual Haken conjecture in the theory of hyperbolic 3-manifolds, there has been much attention devoted to CAT(0) cube complexes. These non-positively curved metric spaces are powerful tools for ...
New Simple Representations of Leavitt Path Algebras
(2019-12-13)
This thesis is about representations of Leavitt Path Algebras (LPAs). Specifically, we first generalize a previously known construction of twisted Chen modules over the Leavitt Path Algebra of a directed graph. We then ...
Arithmetic in Quaternion Algebras and Quaternionic Modular Forms
(2019-05-10)
This dissertation has two parts. In the first part, we revisit the correspondence between spaces of modular forms and orders in quaternion algebras addressed first by Eichler and completed by Hijikata, Pizer, and Shemanske, ...
PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION
(2019-05-10)
We study the existence, uniqueness and stability of solutions to the initial-value problem for the periodic dispersion-managed nonlinear Schr\"{o}dinger (DMNLS) equation, an equation that models the propagation of periodic, ...