Now showing items 31-40 of 66
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 ...
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 ...
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 ...
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 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 ...
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 ...