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

  • Differential Operators on Manifolds with G2-Structure 

    Suan, Caleb (University of Waterloo, 2020-12-16)
    In this thesis, we study differential operators on manifolds with torsion-free G2-structure. In particular, we use an identification of the spinor bundle S of such a manifold M with the bundle R ⊕ T*M to reframe statements ...
  • Sparse Automatic Sets 

    Albayrak, Seda (University of Waterloo, 2020-11-26)
    The theory of automatic sets and sequences arises naturally in many different areas of mathematics, notably in the study of algebraic power series in positive characteristic, due to work of Christol, and in Derksen's ...
  • Coefficient spaces arising from locally compact groups 

    Tanko, Zsolt (University of Waterloo, 2020-08-17)
    This thesis studies two disjoint topics involving coefficient spaces and algebras associated to locally compact groups. First, Chapter 3 investigates the connection between amenability and compactness conditions on locally ...
  • Recurrence in Algebraic Dynamics 

    Hossain, Ehsaan (University of Waterloo, 2020-07-28)
    The Dynamical Mordell--Lang Conjecture states that if a polynomial orbit has infinite intersection with a closed set in an algebraic variety, then the intersection must occur periodically. Although this problem is unsolved ...
  • Some Problems in Multiplicative and Additive Number Theory 

    Elma, Ertan (University of Waterloo, 2020-07-27)
    In this thesis, we obtain several results in number theory. Let $k\geqslant 1$ be a natural number and $\omega_k(n)$ denote the number of distinct prime factors of a natural number $n$ with multiplicity $k$. We estimate ...
  • Applications of Operator Systems in Dynamics, Correlation Sets, and Quantum Graphs 

    Kim, Se Jin (University of Waterloo, 2020-07-24)
    The recent works of Kalantar-Kennedy, Katsoulis-Ramsey, Ozawa, and Dykema-Paulsen have demonstrated that many problems in the theory of operator algebras and quantum information can be approached by looking at various ...
  • Topics in G₂ geometry and geometric flows 

    Dwivedi, Shubham (University of Waterloo, 2020-05-15)
    We study three different problems in this thesis, all related to G₂ structures and geometric flows. In the first problem we study hypersurfaces in a nearly G₂ manifold. We define various quantities associated to such a ...
  • On Hopf Ore Extensions and Zariski Cancellation Problems 

    Huang, Hongdi (University of Waterloo, 2020-04-29)
    In this thesis, we investigate Ore extensions of Hopf algebras and the Zariski Cancellation problem for noncommutative rings. In particular, we improve upon the existing conditions for when $T=R[x; \sigma, \delta]$ is a ...
  • A spatial version of Wedderburn’s Principal Theorem 

    Livshits, L.; MacDonald, G.W.; Marcoux, L.W.; Radjavi, H. (Taylor & Francis, 2015)
    In this article we verify that ‘Wedderburn’s Principal Theorem’ has a particularly pleasant spatial implementation in the case of cleft subalgebras of the algebra of all linear transformations on a finite-dimensional vector ...
  • Universal bounds for positive matrix semigroups 

    Livshits, Leo; MacDonald, Gordon; Marcoux, Laurent; Radjavi, Heydar (Polish Academy of Sciences, 2016)
    We show that any compact semigroup of positive n×n matrices is similar (via a positive diagonal similarity) to a semigroup bounded by n√. We give examples to show this bound is best possible. We also consider the effect ...
  • Reducibility of operator semigroups and values of vector states 

    Marcoux, L.W.; Radjavi, H.; Yahaghi, B.R. (Springer, 2017-08-01)
    Let S be a multiplicative semigroup of bounded linear operators on a complex Hilbert space H, and let Ω be the range of a vector state on S so that Ω = {⟨Sξ, ξ⟩ : S ∈ S} for some fixed unit vector ξ ∈ H. We study the ...
  • Compact ideals and rigidity of representations for amenable operator algebras 

    Clouâtre, Raphaël; Marcoux, Laurent W. (Polish Academy of Sciences, 2019)
    We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison’s conjecture on completely bounded homomorphisms ...
  • Residual finite dimensionality and representations of amenable operator algebras 

    Clouâtre, Raphaël; Marcoux, Laurent W. (Elsevier, 2019-04-15)
    We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable ...
  • Abelian, amenable operator algebras are similar to C∗ -algebras 

    Marcoux, Laurent W.; Popov, Alexey I. (Duke University Press, 2016-12)
    Suppose that H is a complex Hilbert space and that ℬ(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C∗-algebra. We do this by showing that if 𝒜⊆ℬ(H) is ...
  • Ranges of vector states on irreducible operator semigroups 

    Marcoux, L.W.; Omladič, M.; Popov, A.I.; Radjavi, H.; Yahaghi, B. (Springer, 2016)
    Let 𝜑 be a linear functional of rank one acting on an irreducible semigroup S of operators on a finite- or infinite-dimensional Hilbert space. It is a well-known and simple fact that the range of 𝜑 cannot be a singleton. ...
  • On selfadjoint extensions of semigroups of partial isometries 

    Bernik, Janez; Marcoux, Laurent W.; Popov, Alexey I.; Radjavi, Heydar (American Mathematical Society, 2016)
    Let S be a semigroup of partial isometries acting on a complex, infinite- dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup T generated by S consists ...
  • Linear preservers of polynomial numerical hulls of matrices 

    Aghamollaei, Gh.; Marcoux, L.W.; Radjavi, H. (Elsevier, 2019-08-15)
    Let Mn be the algebra of all n × n complex matrices, 1 ≤ k ≤ n − 1 be an integer, and φ : Mn −→ Mn be a linear operator. In this paper, it is shown that φ preserves the polynomial numerical hull of order k if and only if ...
  • Compressible Matrix Algebras and the Distance from Projections to Nilpotents 

    Cramer, Zachary (University of Waterloo, 2019-11-15)
    In this thesis we address two problems from the fields of operator algebras and operator theory. In our first problem, we seek to obtain a description of the unital subalgebras $\mathcal{A}$ of $\mathbb{M}_n(\mathbb{C})$ ...
  • Algebraic Approaches to State Complexity of Regular Operations 

    Davies, Sylvie (University of Waterloo, 2019-10-15)
    The state complexity of operations on regular languages is an active area of research in theoretical computer science. Through connections with algebra, particularly the theory of semigroups and monoids, many problems ...
  • Rational approximations on smooth rational surfaces 

    Castañeda Santos, Diana Carolina (University of Waterloo, 2019-08-09)
    In this thesis, we study a conjecture made by D. McKinnon about rational approximations to rational points in algebraic varieties. The conjecture states that if a rational point P on a variety X lies on a rational curve, ...

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