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Now showing items 1-10 of 16

#### 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 ...

#### 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 ...

#### On the Erdös-Turán conjecture and related results

(University of Waterloo, 2011-08-29)

The Erdös-Turán 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, 2011-12-19)

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 ...

#### 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 ...

#### 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.

#### The Algebraic Kirchberg--Phillips Conjecture for Leavitt Path Algebras

(University of Waterloo, 2015-09-18)

This essay is meant to be an exposition of the theory of Leavitt path algebras and graph C*-algebras, with an aim to discuss some current classification questions. These two classes of algebras sit on opposite sides of a ...

#### Asymptotic Distributions for Block Statistics on Non-crossing Partitions

(University of Waterloo, 2014-01-23)

The set of non-crossing partitions was first studied by Kreweras in 1972 and was known to play an important role in combinatorics, geometric group theory, and free probability. In particular, it has a natural embedding ...