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

  • A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences 

    Murty, M. Ram; Séguin, François; Stewart, Cameron L. (Elsevier, 2019-01-01)
    In 1927, Artin conjectured that any integer other than −1 or a perfect square generates the multiplicative group (Z/pZ)× for infinitely many p. In 2000, Moree and Stevenhagen considered a two-variable version of this ...
  • On fixed points of self maps of the free ball 

    Shamovich, Eli (Elsevier, 2018-07-01)
    In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ...
  • Series-Parallel Posets and Polymorphisms 

    Song, Renzhi (University of Waterloo, 2018-09-04)
    We examine various aspects of the poset retraction problem for series-parallel posets. In particular we show that the poset retraction problem for series-parallel posets that are already solvable in polynomial time are ...
  • Symmetrically-Normed Ideals and Characterizations of Absolutely Norming Operators 

    Pandey, Satish Kumar (University of Waterloo, 2018-08-23)
    The primary objective of this thesis is two fold: first, it is devoted to the study of absolutely norming operators (with respect to various arbitrary symmetric norms on $\mathcal{B}(\mathcal{H})$) with an eye towards the ...
  • Tsirelson's problems and entanglement breaking rank 

    Prakash, Jitendra (University of Waterloo, 2018-08-13)
    There are two main themes of this thesis. In the first part, we study the various sets of correlations arising in the study of non-local games and Tsirelson's problems. In the second part we introduce the notion of ...
  • Abstract and Explicit Constructions of Jacobian Varieties 

    Urbanik, David (University of Waterloo, 2018-08-10)
    Abelian varieties, in particular Jacobian varieties, have long attracted interest in mathematics. Their influence pervades arithmetic geometry and number theory, and understanding their construction was a primary motivator ...
  • Regular Dilation on Semigroups 

    Li, Boyu (University of Waterloo, 2018-08-07)
    Dilation theory originated from Sz.Nagy's celebrated dilation theorem which states that every contractive operator has an isometric dilation. Regular dilation is one of many fruitful directions that aims to generalize ...
  • Problems in Combinatorial and Analytic Number Theory 

    Saunders, John Charles (University of Waterloo, 2018-08-01)
    We focus on three problems in number theory. The first problem studies the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single ...
  • 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 ...

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