Now showing items 1-10 of 22
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 ...
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 ...
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 ...
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 ...
On the local positivity of line bundles on algebraic surfaces
(University of Waterloo, 2015-01-09)
In this thesis, we define a measure for how `positive' an effective line bundle is at a point on a variety, and prove that it is linear on the numerically effective subcone on a smooth, complete, toric surface.
The Eberlein Compactification of Locally Compact Groups
(University of Waterloo, 2013-01-24)
A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection ...
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 ...
Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields
(University of Waterloo, 2010-06-29)
The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational ...