Browsing Pure Mathematics by Issue Date
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Integral Moments of Quadratic Dirichlet Lfunctions: A Computational Perspective
(University of Waterloo, 20100427)In recent years, the moments of Lfunctions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have ... 
Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces
(University of Waterloo, 20100427)We are interested in investigating the number of integral points on quadrics. First, we consider nondegenerate plane conic curves defined over Z. In particular we look at two types of conic sections: hyperbolas with ... 
Settling Time Reducibility Orderings
(University of Waterloo, 20100428)It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets. However, it has been shown that no such ordering can be formed when considering computation ... 
The MordellLang Theorem from the Zilber Dichotomy
(University of Waterloo, 20100430)We present a largely selfcontained exposition of Ehud Hrushovski's proof of the function field MordellLang conjecture beginning from the Zilber Dichotomy for differentially closed fields and separably closed fields. Our ... 
On Transcendence of Irrationals with Noneventually Periodic badic Expansions
(University of Waterloo, 20100518)It is known that almost all numbers are transcendental in the sense of Lebesgue measure. However there is no simple rule to separate transcendental numbers from algebraic numbers. Today research in this direction is about ... 
Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields
(University of Waterloo, 20100629)The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the HardyLittlewood circle method to investigate the density of rational ... 
On Convolution Squares of Singular Measures
(University of Waterloo, 20100825)We prove that if $1 > \alpha > 1/2$, then there exists a probability measure $\mu$ such that the Hausdorff dimension of its support is $\alpha$ and $\mu*\mu$ is a Lipschitz function of class $\alpha1/2$. 
On the Representation Theory of Semisimple Lie Groups
(University of Waterloo, 20100830)This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of BorelWeilBott, CasselmanOsborne and Kostant. The first of these realizes all ... 
Harmonic analysis of Rajchman algebras
(University of Waterloo, 20100831)Abstract harmonic analysis is mainly concerned with the study of locally compact groups, their unitary representations, and the function spaces associated with them. The Fourier and FourierStieltjes algebras are two of ... 
On the Modular Theory of von Neumann Algebras
(University of Waterloo, 20100917)The purpose of this thesis is to provide an exposition of the \textit{modular theory} of von Neumann algebras. The motivation of the theory is to classify and describe von Neumann algebras which do not admit a trace, and ... 
Lower order terms of moments of Lfunctions
(University of Waterloo, 20110617)<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the kth moments of the central values of quadratic Dirichlet Lfunctions. The conjectured formula ... 
Free semigroup algebras and the structure of an isometric tuple
(University of Waterloo, 20110628)An ntuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ... 
Mean Curvature Flow in Euclidean spaces, Lagrangian Mean Curvature Flow, and Conormal Bundles
(University of Waterloo, 20110810)I will present the mean curvature flow in Euclidean spaces and the Lagrangian mean curvature flow. We will first study the mean curvature evolution of submanifolds in Euclidean spaces, with an emphasis on the case of ... 
The LangTrotter conjecture for Drinfeld modules
(University of Waterloo, 20110822)In 1986, Gupta and Murty proved the LangTrotter conjecture in the case of elliptic curves having complex multiplication, conditional on the generalized Riemann hypothesis. That is, given a nontorsion point P∈E(ℚ), they ... 
On the ErdösTurán conjecture and related results
(University of Waterloo, 20110829)The ErdösTurán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ... 
A survey of Roth's Theorem on progressions of length three
(University of Waterloo, 20111219)For any finite set B and a subset A⊆B, we define the density of A in B to be the value α=A/B. Roth's famous theorem, proven in 1953, states that there is a constant C>0, such that if A⊆{1,...,N} for a positive integer ... 
The Fourier algebra of a locally trivial groupoid
(University of Waterloo, 20120110)The goal of this thesis is to define and study the Fourier algebra A(G) of a locally compact groupoid G. If G is a locally compact group, its FourierStieltjes algebra B(G) and its Fourier algebra A(G) were defined by ... 
Geometrical Frustration and Static Correlations in a Simple Glass Former
(American Physical Society, 20120118)We study the geometrical frustration scenario of glass formation for simple hardsphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding ... 
Pick Interpolation and the Distance Formula
(University of Waterloo, 20120509)The classical interpolation theorem for the open complex unit disk, due to Nevanlinna and Pick in the early 20th century, gives an elegant criterion for the solvability of the problem as an eigenvalue problem. In the 1960s, ... 
Representations of Operator Algebras
(University of Waterloo, 20120511)The following thesis is divided into two main chapters. In Chapter 2 we study isometric representations of product systems of correspondences over the semigroup 𝐍ᵏ which are minimal dilations of finite dimensional, fully ...