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Now showing items 1-10 of 38

#### The Cohomology Ring of a Finite Abelian Group

(University of Waterloo, 2013-01-25)

The cohomology ring of a finite cyclic group was explicitly computed by Cartan and Eilenberg in their 1956 book on Homological Algebra. It is surprising that the cohomology ring for the next simplest example, that of a ...

#### 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 ...

#### 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 ...

#### The Lang-Trotter conjecture for Drinfeld modules

(University of Waterloo, 2011-08-22)

In 1986, Gupta and Murty proved the Lang-Trotter conjecture in the case of elliptic curves having complex multiplication, conditional on the generalized Riemann hypothesis. That is, given a non-torsion point P∈E(ℚ), they ...

#### Contributions to the model theory of partial differential fields

(University of Waterloo, 2013-08-28)

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed ...

#### Maximal ideal space techniques in non-selfadjoint operator algebras

(University of Waterloo, 2013-04-26)

The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the ...

#### 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 ...

#### Complexity of Classes of Structures

(University of Waterloo, 2013-08-28)

The main theme of this thesis is studying classes of structures with respect to various measurements of complexity. We will briefly discuss the notion of computable dimension, while the breadth of the paper will focus on ...

#### 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 ...

#### The Fourier algebra of a locally trivial groupoid

(University of Waterloo, 2012-01-10)

The goal of this thesis is to define and study the Fourier algebra A(G) of a locally compact groupoid G. If G is a locally compact group, its Fourier-Stieltjes algebra B(G) and its Fourier algebra A(G) were defined by ...