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#### Harmonic analysis of Rajchman algebras

(University of Waterloo, 2010-08-31)

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 Fourier-Stieltjes algebras are two of ...

#### Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces

(University of Waterloo, 2010-04-27)

We are interested in investigating the number of integral points on quadrics.
First, we consider non-degenerate plane conic curves defined over Z.
In particular we look at two types of conic sections: hyperbolas with ...

#### On Transcendence of Irrationals with Non-eventually Periodic b-adic Expansions

(University of Waterloo, 2010-05-18)

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 ...

#### The Mordell-Lang Theorem from the Zilber Dichotomy

(University of Waterloo, 2010-04-30)

We present a largely self-contained exposition of Ehud Hrushovski's proof of the function field Mordell-Lang conjecture beginning from the Zilber Dichotomy for differentially closed fields and separably closed fields. Our ...

#### Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective

(University of Waterloo, 2010-04-27)

In recent years, the moments of L-functions 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 ...

#### On the Modular Theory of von Neumann Algebras

(University of Waterloo, 2010-09-17)

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 ...

#### On Convolution Squares of Singular Measures

(University of Waterloo, 2010-08-25)

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 $\alpha-1/2$.

#### Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields

(University of Waterloo, 2010-06-29)

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 Hardy-Littlewood circle method to investigate the density of rational ...

#### Settling Time Reducibility Orderings

(University of Waterloo, 2010-04-28)

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 ...

#### On the Representation Theory of Semisimple Lie Groups

(University of Waterloo, 2010-08-30)

This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all ...