Now showing items 21-40 of 165

    • Para-Holomorphic Algebroids and Para-Complex Connections 

      Patterson, Aidan (University of Waterloo, 2021-12-17)
      The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold ...
    • Exact Formulas for Averages of Secular Coefficients 

      Medjedovic, Andean (University of Waterloo, 2021-09-29)
      We study averages of secular coefficients that frequently appear in random matrix theory. We obtain exact formulas, identities and new asymptotics for these integrals as well as a technique to deal with singularities that ...
    • A guide to F-automatic sets 

      Hawthorne, Christopher (University of Waterloo, 2021-09-08)
      A self-contained introduction to the theory of F-automatic sets is given. Building on [Bell, Moosa, F-sets and finite automata, Journal de théorie des nombres de Bordeaux, 2019], contributions are made to both the foundations ...
    • Applications of the minimal modelprogram in arithmetic dynamics 

      Nasserden, Brett (University of Waterloo, 2021-09-07)
      Let F be a surjective endomorphism of a normal projective variety X defined over a number field. The dynamics of F may be studied through the dynamics of the linear action of an associated linear pull-back action on divisors. ...
    • Deformation theory of nearly G₂-structures and nearly G₂ instantons 

      Singhal, Ragini (University of Waterloo, 2021-08-30)
      We study two different deformation theory problems on manifolds with a nearly G₂-structure. The first involves studying the deformation theory of nearly G₂ manifolds. These are seven dimensional manifolds admitting real ...
    • On the structure of invertible elements in certain Fourier-Stieltjes algebras 

      Thamizhazhagan, Aasaimani (University of Waterloo, 2021-08-27)
      Let $G$ be a locally compact group. The Fourier-Stieltjes and Fourier algebras, $B(G)$ and $A(G)$ are defined by Eymard to act as dual objects of the measure and group algebras, $M(G)$ and $L^1(G)$, in a sense generalizing ...
    • Trisections of non-orientable 4-manifolds 

      Naylor, Patrick (University of Waterloo, 2021-08-24)
      Broadly, this thesis is concerned with trying to understand 4-manifolds through 3-dimensional techniques. From the point of view of smooth manifolds, dimension four is quite unique; one striking illustration of this is the ...
    • 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 ...

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