Now showing items 1-20 of 113

    • 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 ...
    • Degrees of Categoricity and the Isomorphism Problem 

      Mahmoud, Mohammad (University of Waterloo, 2019-06-12)
      In this thesis, we study notions of complexity related to computable structures. We first study degrees of categoricity for computable tree structures. We show that, for any computable ordinal $\alpha$, there exists a ...
    • Sidon and Kronecker-like sets in compact abelian groups 

      Yang, Xu (University of Waterloo, 2019-06-07)
      Let $G$ be a compact abelian group and $\Ga$ be its discrete dual group. In this thesis we study various types of interpolation sets. A subset $E \subset \Ga$ is Sidon if every bounded function on $E$ can be interpolated ...
    • The Logarithmic Derivative and Model-Theoretic Analysability in Differentially Closed Fields 

      Jin, Ruizhang (University of Waterloo, 2019-01-22)
      This thesis deals with internal and analysable types, mainly in the context of the stable theory of differentially closed fields. Two main problems are dealt with: the construction of types analysable in the constants with ...
    • Compressions of Compact Tuples 

      Passer, Benjamin; Shalit, Orr (Elsevier, 2019-03-01)
      We study the matrix range of a tuple of compact operators on a Hilbert space and examine the notions of minimal, nonsingular, and fully compressed tuples. In this pursuit, we refine previous results by characterizing ...
    • 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 ...

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