Pure Mathematics
This is the collection for the University of Waterloo's Department of Pure Mathematics .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
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Compressions of Compact Tuples
(Elsevier, 20190301)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 twovariable Artin conjecture and prime divisors of recurrence sequences
(Elsevier, 20190101)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 twovariable version of this ... 
On fixed points of self maps of the free ball
(Elsevier, 20180701)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 ... 
SeriesParallel Posets and Polymorphisms
(University of Waterloo, 20180904)We examine various aspects of the poset retraction problem for seriesparallel posets. In particular we show that the poset retraction problem for seriesparallel posets that are already solvable in polynomial time are ... 
SymmetricallyNormed Ideals and Characterizations of Absolutely Norming Operators
(University of Waterloo, 20180823)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
(University of Waterloo, 20180813)There are two main themes of this thesis. In the first part, we study the various sets of correlations arising in the study of nonlocal games and Tsirelson's problems. In the second part we introduce the notion of ... 
Abstract and Explicit Constructions of Jacobian Varieties
(University of Waterloo, 20180810)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
(University of Waterloo, 20180807)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
(University of Waterloo, 20180801)We focus on three problems in number theory. The first problem studies the random Fibonacci tree, which is an infinite binary tree with nonnegative integers at each node. The root consists of the number 1 with a single ... 
Weak Moment Maps in Multisymplectic Geometry
(University of Waterloo, 20180704)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
(Elsevier, 20180901)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
(University of Waterloo, 20180122)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
(University of Waterloo, 20170828)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 GStructures
(University of Waterloo, 20170824)In this thesis, we study the integrability problem for Gstructures. Broadly speaking, this is the problem of determining topological obstructions to the existence of principal Gsubbundles of the frame bundle of a manifold, ... 
2Semilattices: Residual Properties and Applications to the Constraint Satisfaction Problem
(University of Waterloo, 20170822)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
(University of Waterloo, 20170818)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 ... 
Techniques in operator algebras: classification, dilation and noncommutative boundary theory
(University of Waterloo, 20170811)In this thesis we bring together several techniques in the theory of nonselfadjoint operator algebras and operator systems. We begin with classification of nonselfadjoint and selfadjoint operator algebras constructed ... 
The Liftable Mapping Class Group
(University of Waterloo, 20170719)Broadly, this thesis lies at the interface of mapping class groups and covering spaces. The foundations of this area were laid down in the early 1970s by Birman and Hilden. Building on these foundations, there has been a ... 
Contributions to the Theory of Radicals for Noncommutative Rings
(University of Waterloo, 20170620)We consider several radical classes of noncommutative rings. In particular, we provide new results regarding the radical theory of semigroupgraded rings, monomial algebras, and Ore extensions of derivation type. In ... 
Geometrical frustration and static correlations in hardsphere glass formers
(American Institute of Physics, 20130328)We analytically and numerically characterize the structure of hardsphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated ...