## Search

Now showing items 11-20 of 66

#### Semistable rank 2 co-Higgs bundles over Hirzebruch surfaces

(University of Waterloo, 2015-08-07)

It has been observed by S. Rayan that the complex projective surfaces that potentially
admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end
of the Enriques-Kodaira classification. ...

#### 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 ...

#### Koblitz's Conjecture for the Drinfeld Module

(University of Waterloo, 2008-05-01)

Let $E$ be an elliptic curve over the rationals without complex multiplication such that any elliptic curve $\mathbb{Q}$-isogenous to $E$ has trivial $\mathbb{Q}$-torsion. Koblitz conjectured that the number of primes less ...

#### On a Question of Wintner Concerning the Sequence of Integers Composed of Primes from a Given Set

(University of Waterloo, 2007-09-27)

We answer to a Wintner's question
concerning the sequence of integers
composed of primes from a given set.
The results generalize and develop the answer to Wintner’s question due to
Tijdeman.