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

Recent Submissions

  • On Asynchronous Interference Channels 

    Moshksar, Kamyar (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 

    Faint, Stephanie (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, ...

    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 ...

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