Now showing items 1-20 of 165

    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Algebraic characterization of multivariable dynamics 

      Ramsey, Christopher (University of Waterloo, 2009-03-26)
      Let X be a locally compact Hausdorff space along with n proper continuous maps σ = (σ1 , · · · , σn ). Then the pair (X, σ) is called a dynamical system. To each system one can associate a universal operator algebra called ...
    • ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS 

      Bernik, Janez; Livshits, Leo; MacDonald, Gordon W.; Marcoux, Laurent W.; Mastnak, Mitja; Radjavi, Heydar (American Mathematical Society, 2021-07-20)
      We study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly ...
    • 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 ...
    • Amenability for the Fourier Algebra 

      Tikuisis, Aaron Peter (University of Waterloo, 2007-08-29)
      The Fourier algebra A(G) can be viewed as a dual object for the group G and, in turn, for the group algebra L1(G). It is a commutative Banach algebra constructed using the representation theory of the group, and from which ...
    • 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 ...
    • 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. ...
    • Approximation Constants for Closed Subschemes of Projective Varieties 

      Rollick, Nickolas (University of Waterloo, 2019-06-19)
      Diophantine approximation is a branch of number theory with a long history, going back at least to the work of Dirichlet and Liouville in the 1840s. The innocent-looking question of how well an arbitrary real algebraic ...
    • Artin's Conjecture: Unconditional Approach and Elliptic Analogue 

      Sen Gupta, Sourav (University of Waterloo, 2008-08-11)
      In this thesis, I have explored the different approaches towards proving Artin's `primitive root' conjecture unconditionally and the elliptic curve analogue of the same. This conjecture was posed by E. Artin in the year ...
    • Artin's Primitive Root Conjecture and its Extension to Compositie Moduli 

      Camire, Patrice (University of Waterloo, 2008-08-11)
      If we fix an integer a not equal to -1 and which is not a perfect square, we are interested in estimating the quantity N_{a}(x) representing the number of prime integers p up to x such that a is a generator of the cyclic ...
    • 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 ...
    • Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields 

      Zhao, Xiaomei (University of Waterloo, 2010-06-29)
      The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational ...
    • Branched Covering Constructions and the Symplectic Geography Problem 

      Hughes, Mark Clifford (University of Waterloo, 2008-08-15)
      We apply branched covering techniques to construct minimal simply-connected symplectic 4-manifolds with small χ_h values. We also use these constructions to provide an alternate proof that for each s ≥ 0, there exists a ...
    • Brands of cumulants in non-commutative probability, and relations between them 

      Perales, Daniel (University of Waterloo, 2022-07-06)
      The study of non-commutative probability revolves around the different notions of independeces, such as free, Boolean and monotone. To each type of independence one can associate a notion of cumulants that linearize the ...
    • 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].
    • 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 ...
    • Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Field and R) 

      Gong, Ming-Peng (University of Waterloo, 1998)
      This thesis is concerned with the classification of 7-dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension <i>n</i> given those ...

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