Pure Mathematics
This is the collection for the University of Waterloo's Department of Pure Mathematics .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
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Semicrossed Products, Dilations, and Jacobson Radicals
(University of Waterloo, 20170818)We compute the C*envelope of the isometric semicrossed product of a C*algebra arising from number theory by the multiplicative semigroup of a number ring R, and prove that it is isomorphic to T[R], the left regular ... 
Techniques in operator algebras: classification, dilation and noncommutative boundary theory
(University of Waterloo, 20170811)In this thesis we bring together several techniques in the theory of nonselfadjoint operator algebras and operator systems. We begin with classification of nonselfadjoint and selfadjoint operator algebras constructed ... 
The Liftable Mapping Class Group
(University of Waterloo, 20170719)Broadly, this thesis lies at the interface of mapping class groups and covering spaces. The foundations of this area were laid down in the early 1970s by Birman and Hilden. Building on these foundations, there has been a ... 
Contributions to the Theory of Radicals for Noncommutative Rings
(University of Waterloo, 20170620)We consider several radical classes of noncommutative rings. In particular, we provide new results regarding the radical theory of semigroupgraded rings, monomial algebras, and Ore extensions of derivation type. In ... 
Geometrical frustration and static correlations in hardsphere glass formers
(American Institute of Physics, 20130328)We analytically and numerically characterize the structure of hardsphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated ... 
Geometrical Frustration and Static Correlations in a Simple Glass Former
(American Physical Society, 20120118)We study the geometrical frustration scenario of glass formation for simple hardsphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding ... 
Dimensional dependence of the StokesEinstein relation and its violation
(American Institute of Physics, 20131028)We generalize to higher spatial dimensions the StokesEinstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical ... 
On Asynchronous Interference Channels
(University of Waterloo, 20161115)In the first part of the thesis, a decentralized wireless network of separate transmitterreceiver pairs is studied where there is no central controller to assign the resources to the users and users do not explicitly ... 
The Enigma History and Mathematics
(University of Waterloo, 20161025)In this thesis we look at the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, ... 
COMPATIBILITY OF EXTENSIONS OF A COMBINATORIAL GEOMETRY
(University of Waterloo, 20160929)Two extensions of a geometry are compatible with each other if they have a common extension. If the given extensions are elementary, their compatibility can be intrinsically described in terms of their corresponding linear ... 
Classical Field Theory in the BV Formalism
(University of Waterloo, 20160920)This document is a review of the perspective on classical eld theories presented in [2] and [3]. 
Strong Morita Equivalence and Imprimitivity Theorems
(University of Waterloo, 20160915)The purpose of this thesis is to give an exposition of two topics, mostly following the books \cite{R & W} and \cite{Wil}. First, we wish to investigate crossed product $C^*$algebras in its most general form. Crossed ... 
Graph C*algebras and the Abelian Core
(University of Waterloo, 20160826)We may associate to a C*algebra to the directed graph E by associating edges to partial isometries and vertices to pairwise orthogonal Hilbert spaces which satisfy some additional conditions. Such graph algebras were first ... 
Some results on binary forms and counting rational points on algebraic varieties
(University of Waterloo, 20160817)In this thesis we study several problems related to the representation of integers by binary forms and counting rational points on algebraic varieties. In particular, we establish an asymptotic formula for $R_F(Z)$, the ... 
NevanlinnaPick Spaces and Dilations
(University of Waterloo, 20160712)The majority of this thesis is devoted to the study of NevanlinnaPick spaces and their multiplier algebras. These spaces are Hilbert function spaces in which a version of the NevanlinnaPick interpolation theorem from ... 
Exotic Group C*algebras, Tensor Products, and Related Constructions
(University of Waterloo, 20160615)Recently there has been a rejuvenated interest in exotic group C*algebras, i.e., group C*algebras which are "intermediate" to the full and reduced group C*algebras. This resurgence began with the introduction of the ... 
The Algebraic KirchbergPhillips Conjecture for Leavitt Path Algebras
(University of Waterloo, 20150918)This essay is meant to be an exposition of the theory of Leavitt path algebras and graph C*algebras, with an aim to discuss some current classification questions. These two classes of algebras sit on opposite sides of a ... 
Elliptic Curves over Finite Fields and their lTorsion Galois Representations
(University of Waterloo, 20150908)Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ... 
Some additive results in F_q[t]
(University of Waterloo, 20150827)We collected several results in integers of additive number theory and translated to results in F_q[t]. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, a ... 
Semistable rank 2 coHiggs bundles over Hirzebruch surfaces
(University of Waterloo, 20150807)It has been observed by S. Rayan that the complex projective surfaces that potentially admit nontrivial examples of semistable coHiggs bundles must be found at the lower end of the EnriquesKodaira classification. ...