This is the collection for the University of Waterloo's Department of Pure Mathematics theses & dissertations.

Graduate students can submit a copy of their electronic thesis or dissertation to this collection to meet their degree requirements.

Recent Submissions


    Cheung, Alan (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 

    Butson, Dylan (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 

    Kim, Se-Jin (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 

    Eifler, Kari (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 

    Xiao, Stanley Yao (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 

    Hartz, Michael Peter (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 

    Wiersma, Matthew (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 

    Hossain, Ehsaan (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 

    Baker, Michael (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] 

    Yamagishi, Shuntaro (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 

    Vicente Colmenares, Alejandra (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 

    Xiao, Rui Philip (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 

    Garbary, Robert (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 

    Yang, Xu (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.
  • Generalized Complex Structures on Kodaira Surfaces 

    Hamilton, Jordan (University of Waterloo, 2014-08-05)
    In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized ...
  • Families of Thue Inequalities with Transitive Automorphisms 

    An, Wenyong (University of Waterloo, 2014-06-17)
    A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by ...
  • Some aspects of Cantor sets 

    Ng, Ka Shing (University of Waterloo, 2014-03-28)
    For every positive, decreasing, summable sequence $a=(a_i)$, we can construct a Cantor set $C_a$ associated with $a$. These Cantor sets are not necessarily self-similar. Their dimensional properties and measures have been ...
  • Asymptotic Distributions for Block Statistics on Non-crossing Partitions 

    Li, Boyu (University of Waterloo, 2014-01-23)
    The set of non-crossing partitions was first studied by Kreweras in 1972 and was known to play an important role in combinatorics, geometric group theory, and free probability. In particular, it has a natural embedding ...
  • Contributions to the model theory of partial differential fields 

    Leon Sanchez, Omar (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 ...
  • Complexity of Classes of Structures 

    Knoll, Carolyn (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 ...

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