Browsing Pure Mathematics by Type "Doctoral Thesis"
Now showing items 1-20 of 77
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2-Semilattices: Residual Properties and Applications to the Constraint Satisfaction Problem
(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 ... -
Algebraic Approaches to State Complexity of Regular Operations
(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 ... -
Applications of Operator Systems in Dynamics, Correlation Sets, and Quantum Graphs
(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
(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
(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 ... -
Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields
(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 ... -
Brands of cumulants in non-commutative probability, and relations between them
(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 ... -
Classification of Finitely Generated Operator Systems
(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)
(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 ... -
Coefficient spaces arising from locally compact groups
(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 ... -
The Cohomology Ring of a Finite Abelian Group
(University of Waterloo, 2013-01-25)The cohomology ring of a finite cyclic group was explicitly computed by Cartan and Eilenberg in their 1956 book on Homological Algebra. It is surprising that the cohomology ring for the next simplest example, that of a ... -
COMPATIBILITY OF EXTENSIONS OF A COMBINATORIAL GEOMETRY
(University of Waterloo, 2016-09-29)Two extensions of a geometry are compatible with each other if they have a common extension. If the given extensions are elementary, their compatibility can be intrinsically described in terms of their corresponding linear ... -
Complexity of Classes of Structures
(University of Waterloo, 2013-08-28)The main theme of this thesis is studying classes of structures with respect to various measurements of complexity. We will briefly discuss the notion of computable dimension, while the breadth of the paper will focus on ... -
Compressible Matrix Algebras and the Distance from Projections to Nilpotents
(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 $\mathbb{M}_n(\mathbb{C})$ ... -
Computability Theory and Some Applications
(University of Waterloo, 2019-07-15)We explore various areas of computability theory, ranging from applications in computable structure theory primarily focused on problems about computing isomorphisms, to a number of new results regarding the degree-theoretic ... -
Contributions to the model theory of partial differential fields
(University of Waterloo, 2013-08-28)In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed ... -
Contributions to the Theory of Radicals for Noncommutative Rings
(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 ... -
Deformation theory of nearly G₂-structures and nearly G₂ instantons
(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 ... -
Degrees of Categoricity and the Isomorphism Problem
(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 ... -
Digraph Algebras over Discrete Pre-ordered Groups
(University of Waterloo, 2013-01-25)This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital ...