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Now showing items 1-10 of 39

#### Generalisations of Roth's theorem on finite abelian groups

(University of Waterloo, 2012-12-18)

Roth's theorem, proved by Roth in 1953, states that when A is a subset of the integers [1,N] with A dense enough, A has a three term arithmetic progression (3-AP). Since then the bound originally given by Roth has been ...

#### K-theory for C*-Algebras and for Topological Spaces

(University of Waterloo, 2015-04-27)

K-theory is the study of a collection of abelian groups that are invariant to C*-algebras or to locally compact Hausdorff spaces. These groups are useful for distinguishing C*-algebras and topological spaces, and they are ...

#### 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 ...

#### The Differential Geometry of Instantons

(University of Waterloo, 2009-08-07)

The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge ...

#### Interpolation Sets For Compact Abelian Groups

(University of Waterloo, 2014-09-04)

We will study various properties of I_0 and \epsilon-Kronecker sets.
We show that most infinite sets in the discrete dual group contain infinite interpolation sets.

#### 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 ...

#### Mean Curvature Flow in Euclidean spaces, Lagrangian Mean Curvature Flow, and Conormal Bundles

(University of Waterloo, 2011-08-10)

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 ...

#### Operator Theoretic Methods in Nevanlinna-Pick Interpolation

(University of Waterloo, 2009-03-31)

This Master's thesis will develops a modern approach to complex interpolation problems studied by Carath\'{e}odory, Nevanlinna, Pick, and Schur in the early $20^{th}$ century. The fundamental problem to solve is as follows: ...

#### 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 ...