Browsing Pure Mathematics by Title
Now showing items 21-40 of 165
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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> ... -
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 ... -
Degree Spectra of Unary relations on ω and ζ
(University of Waterloo, 2009-08-13)Let X be a unary relation on the domain of (ω,<). The degree spectrum of X on (ω,<) is the set of Turing degrees of the image of X in all computable presentations of (ω,<). Many results are known about the types of degree ... -
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 ... -
Derived Geometry and the Integrability Problem for G-Structures
(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, ... -
The Differential Geometry of Instantons
(University of Waterloo, 2009-08-07)The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge ... -
Differential Operators on Manifolds with G2-Structure
(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 ... -
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 ... -
Dilation methods in semigroup dynamics and noncommutative convexity
(University of Waterloo, 2022-08-25)Since seminal work of Stinespring, Arveson, and others, dilation theory has been an indispensable tool for understanding operator algebras. Dilations are fundamental to the representation theory of operator systems and ... -
Dimensional dependence of the Stokes-Einstein relation and its violation
(American Institute of Physics, 2013-10-28)We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical ...