## Search

Now showing items 1-10 of 39

#### 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 ...

#### Elliptic Curves over Finite Fields and their l-Torsion Galois Representations

(University of Waterloo, 2015-09-08)

Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ...

#### 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 ...

#### 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 ...

#### Artin's Conjecture: Unconditional Approach and Elliptic Analogue

(University of Waterloo, 2008-08-11)

In this thesis, I have explored the different approaches towards proving Artin's
`primitive root' conjecture unconditionally and the elliptic curve analogue of the
same. This conjecture was posed by E. Artin in the year ...

#### The Normal Distribution of ω(φ(m)) in Function Fields

(University of Waterloo, 2008-01-28)

Let ω(m) be the number of distinct prime factors of m. A
celebrated theorem of Erdös-Kac states that the quantity
(ω(m)-loglog m)/√(loglog m) distributes
normally. Let φ(m) be Euler's φ-function. Erdös and
Pomerance ...

#### Operator Spaces and Ideals in Fourier Algebras

(University of Waterloo, 2008-08-11)

In this thesis we study ideals in the Fourier algebra, A(G), of a
locally compact group G.
For a locally compact abelian group G, necessary conditions for a
closed ideal in A(G) to be weakly complemented are given, ...

#### Branched Covering Constructions and the Symplectic Geography Problem

(University of Waterloo, 2008-08-15)

We apply branched covering techniques to construct minimal simply-connected symplectic 4-manifolds with small χ_h values. We also use these constructions to provide an alternate proof that for each s ≥ 0, there exists a ...

#### A Survey of the Classification of Division Algebras

(University of Waterloo, 2008-09-29)

For a given field F we seek all division algebras over F up to isomorphism. This question was first investigated for division algebras of finite dimension over F by Richard Brauer. We discuss the construction of the Brauer ...

#### Amenability for the Fourier Algebra

(University of Waterloo, 2007-08-29)

The Fourier algebra A(G) can be viewed as a dual object for the group G and, in turn, for the group algebra L1(G). It is a commutative Banach algebra constructed using the representation theory of the group, and from which ...