Browsing Pure Mathematics by Title
Now showing items 12-31 of 165
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Artin's Conjecture: Unconditional Approach and Elliptic Analogue
(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
(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
(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
(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
(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
(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
(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
(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 ... -
Compact ideals and rigidity of representations for amenable operator algebras
(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 ... -
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 $\mathbb{M}_n(\mathbb{C})$ ... -
Compressions of Compact Tuples
(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 ... -
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 ... -
Counting points of bounded height on del Pezzo surfaces
(University of Waterloo, 2006)del Pezzo surfaces are isomorphic to either P<sup>1</sup> x P<sup>1</sup> or P<sup>2</sup> blown up <i>a</i> times, where <i>a</i> ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P<sup>2</sup> ...