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.

Recent deposits

  • Weak Moment Maps in Multisymplectic Geometry 

    Herman, Jonathan (University of Waterloo, 2018-07-04)
    We introduce the notion of a weak (homotopy) moment map associated to a Lie group action on a multisymplectic manifold. We show that the existence/uniqueness theory governing these maps is a direct generalization from ...
  • Existence and uniqueness of weak homotopy moment maps 

    Herman, Jonathan (Elsevier, 2018-09-01)
    We show that the classical results on the existence and uniqueness of moment maps in symplectic geometry generalize directly to weak homotopy moment maps in multisymplectic geometry. In particular, we show that their ...
  • Classification of Finitely Generated Operator Systems 

    Hamzo, Chadi (University of Waterloo, 2018-01-22)
    For the past few decades operator systems and their C*-envelopes have provided an invaluable tool for studying the theory of C*-algebras and positive maps. They provide the natural context in which to study the theory of ...
  • A Parallel Study of the Fock Space Approach to Classical and Free Brownian Motion 

    Hsueh, Kun-Hung (University of Waterloo, 2017-08-28)
    The purpose of this thesis is to elaborate the similarities between the classical and the free probability by means of developing the chaos decomposition of stochastic integrals driven by Brownian motion and its free ...
  • Derived Geometry and the Integrability Problem for G-Structures 

    McCormick, Anthony (University of Waterloo, 2017-08-24)
    In this thesis, we study the integrability problem for G-structures. Broadly speaking, this is the problem of determining topological obstructions to the existence of principal G-subbundles of the frame bundle of a manifold, ...
  • 2-Semilattices: Residual Properties and Applications to the Constraint Satisfaction Problem 

    Payne, Ian (University of Waterloo, 2017-08-22)
    Semilattices are algebras known to have an important connection to partially ordered sets. In particular, if a partially ordered set $(A,\leq)$ has greatest lower bounds, a semilattice $(A;\wedge)$ can be associated to the ...
  • Semicrossed Products, Dilations, and Jacobson Radicals 

    Wiart, Jaspar (University of Waterloo, 2017-08-18)
    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 non-commutative boundary theory 

    Dor On, Adam (University of Waterloo, 2017-08-11)
    In this thesis we bring together several techniques in the theory of non-self-adjoint operator algebras and operator systems. We begin with classification of non-self-adjoint and self-adjoint operator algebras constructed ...
  • The Liftable Mapping Class Group 

    Ghaswala, Tyrone (University of Waterloo, 2017-07-19)
    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 

    Madill, Blake (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 

    Charbonneau, Benoit; Charbonneau, Patrick; Tarjus, Gilles (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 

    Charbonneau, Benoit; Charbonneau, Patrick; Tarjus, Gilles (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 

    Charbonneau, Benoit; Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco (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 

    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 ...

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