Browsing Pure Mathematics by Title
Now showing items 52-71 of 165
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Families of Thue Inequalities with Transitive Automorphisms
(University of Waterloo, 2014-06-17)A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by ... -
Finitary approximations of free probability, involving combinatorial representation theory
(University of Waterloo, 2023-05-18)This thesis contributes to two theories which approximate free probability by finitary combinatorial structures. The first is finite free probability, which is concerned with expected characteristic polynomials of various ... -
The Fourier algebra of a locally trivial groupoid
(University of Waterloo, 2012-01-10)The goal of this thesis is to define and study the Fourier algebra A(G) of a locally compact groupoid G. If G is a locally compact group, its Fourier-Stieltjes algebra B(G) and its Fourier algebra A(G) were defined by ... -
Free semigroup algebras and the structure of an isometric tuple
(University of Waterloo, 2011-06-28)An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ... -
Generalisations of Roth's theorem on finite abelian groups
(University of Waterloo, 2012-12-18)Roth's theorem, proved by Roth in 1953, states that when A is a subset of the integers [1,N] with A dense enough, A has a three term arithmetic progression (3-AP). Since then the bound originally given by Roth has been ... -
Generalizations of the Gap Principle and the Thue-Siegel Principle, with Applications to Diophantine Equations
(University of Waterloo, 2019-07-16)In this thesis we develop generalizations of two well-known principles from the theory of Diophantine approximation, namely the gap principle and the Thue-Siegel principle. Our results find their applications in the theory ... -
Generalized Complex Structures on Kodaira Surfaces
(University of Waterloo, 2014-08-05)In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized ... -
Generalized GCDs as Applications of Vojta’s Conjecture
(University of Waterloo, 2023-08-31)Starting with an analysis of the result that for any coprime integers a and b, and some ϵ > 0, we have eventually that gcd(a^n − 1,b^n − 1) < a^ϵn holds for all n, we are motivated to look for geometric reasons why this ... -
Geometrical Frustration and Static Correlations in a Simple Glass Former
(American Physical Society, 2012-01-18)We study the geometrical frustration scenario of glass formation for simple hard-sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding ... -
Geometrical frustration and static correlations in hard-sphere glass formers
(American Institute of Physics, 2013-03-28)We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated ... -
Graph C*-algebras and the Abelian Core
(University of Waterloo, 2016-08-26)We may associate to a C*-algebra to the directed graph E by associating edges to partial isometries and vertices to pairwise orthogonal Hilbert spaces which satisfy some additional conditions. Such graph algebras were first ... -
Gröbner Bases Theory and The Diamond Lemma
(University of Waterloo, 2006)Commutative Gröbner bases theory is well known and widely used. In this thesis, we will discuss thoroughly its generalization to noncommutative polynomial ring <em>k</em><<em>X</em>> which is also an associative free ... -
A guide to F-automatic sets
(University of Waterloo, 2021-09-08)A self-contained introduction to the theory of F-automatic sets is given. Building on [Bell, Moosa, F-sets and finite automata, Journal de théorie des nombres de Bordeaux, 2019], contributions are made to both the foundations ... -
Harmonic analysis of Rajchman algebras
(University of Waterloo, 2010-08-31)Abstract harmonic analysis is mainly concerned with the study of locally compact groups, their unitary representations, and the function spaces associated with them. The Fourier and Fourier-Stieltjes algebras are two of ... -
Higher-Dimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1
(University of Waterloo, 2007-08-29)We consider the greatest prime factors of integers of certain form. -
Hilbert space operators with compatible off-diagonal corners
(Elsevier, 2018-08-15)Given a complex, separable Hilbert space H, we characterize those operators for which ‖PT(I−P)‖=‖(I−P)TP‖ for all orthogonal projections P on H. When H is finite-dimensional, we also obtain a complete characterization of ... -
Infinite Sets of D-integral Points on Projective Algebrain Varieties
(University of Waterloo, 2005)Let <em>X</em>(<em>K</em>) ⊂ <strong>P</strong><sup><em>n</em></sup> (<em>K</em>) be a projective algebraic variety over <em>K</em>, and let <em>D</em> be a subset of <strong>P</strong><sup><em>n</em></sup><sub><em>O ... -
Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective
(University of Waterloo, 2010-04-27)In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have ... -
Integrality theorems for symmetric instantons
(University of Waterloo, 2022-08-05)Anti-self-dual (ASD) instantons on R4 are connections A on SU(N)-vector bundles with finite L2-norm and curvature satisfying the ASD equation. Solutions to this non-linear partial differential equation correspond to certain ... -
Interpolation Sets For Compact Abelian Groups
(University of Waterloo, 2014-09-04)We will study various properties of I_0 and \epsilon-Kronecker sets. We show that most infinite sets in the discrete dual group contain infinite interpolation sets.