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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).

Recent Submissions

• Contributions to the Theory of Radicals for Noncommutative Rings ﻿

(University of Waterloo, 2017-06-20)
We consider several radical classes of noncommutative rings. In particular, we provide new results regarding the radical theory of semigroup-graded rings, monomial algebras, and Ore extensions of derivation type. In ...
• Geometrical frustration and static correlations in hard-sphere glass formers ﻿

(American Institute of Physics, 2013-03-28)
We analytically and numerically characterize the structure of hard-sphere 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, 2012-01-18)
We study the geometrical frustration scenario of glass formation for simple hard-sphere 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 Stokes-Einstein relation and its violation ﻿

(American Institute of Physics, 2013-10-28)
We generalize to higher spatial dimensions the Stokes-Einstein 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, 2016-11-15)
In the first part of the thesis, a decentralized wireless network of separate transmitter-receiver 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, 2016-10-25)
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, 2016-09-29)
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, 2016-09-20)
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, 2016-09-15)
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, 2016-08-26)
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, 2016-08-17)
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 ...
• Nevanlinna-Pick Spaces and Dilations ﻿

(University of Waterloo, 2016-07-12)
The majority of this thesis is devoted to the study of Nevanlinna-Pick spaces and their multiplier algebras. These spaces are Hilbert function spaces in which a version of the Nevanlinna-Pick interpolation theorem from ...
• Exotic Group C*-algebras, Tensor Products, and Related Constructions ﻿

(University of Waterloo, 2016-06-15)
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 Kirchberg--Phillips Conjecture for Leavitt Path Algebras ﻿

(University of Waterloo, 2015-09-18)
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 l-Torsion Galois Representations ﻿

(University of Waterloo, 2015-09-08)
Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of \$\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ...
• Some additive results in F_q[t] ﻿

(University of Waterloo, 2015-08-27)
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 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. ...
• 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 ...
• 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.
• Interpolation Sets For Compact Abelian Groups ﻿

(University of Waterloo, 2014-09-04)
We will study various properties of I_0 and \epsilon-Kronecker sets. We show that most infinite sets in the discrete dual group contain infinite interpolation sets.

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