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.
Recent deposits

Exactness and Noncommutative Convexity
(University of Waterloo, 20220902)This thesis studies two separate topics in connection to operator systems theory: the dynamics of locally compact groups, and noncommutative convex geometry. In Chapter 1 we study exactness of locally compact groups as ... 
Dilation methods in semigroup dynamics and noncommutative convexity
(University of Waterloo, 20220825)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 ... 
Tracial and ideal structure of crossed products and related constructions
(University of Waterloo, 20220817)In this thesis, we concern ourselves with asking questions about the basic structure of group C*algebras, crossed products, and groupoid C*algebras. Specifically, we are concerned with two main topics. One is the simplicity ... 
On the Dynamical WilfZeilberger Problem
(University of Waterloo, 20220815)In this paper, we give an algorithmic solution to a dynamical analog of the problem of certifying combinatorial identities by WilfZeilberger pairs. Given two sequences generated in a dynamical setting, we calculate an ... 
Integrality theorems for symmetric instantons
(University of Waterloo, 20220805)Antiselfdual (ASD) instantons on R4 are connections A on SU(N)vector bundles with finite L2norm and curvature satisfying the ASD equation. Solutions to this nonlinear partial differential equation correspond to certain ... 
On Amenability Properties and Coideals of Quantum Groups
(University of Waterloo, 20220727)We study amenability type properties of locally compact quantum groups and subobjects of quantum groups realized as submodules of their von Neumann algebras. An important class of such subobjects are the coideals, which ... 
Brands of cumulants in noncommutative probability, and relations between them
(University of Waterloo, 20220706)The study of noncommutative 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 ... 
Dispersing representations of semisimple subalgebras of complex matrices
(Elsevier, 20220601)In this paper we consider the problem of determining the maximum dimension of P?(A!B)P, where A and B are unital, semisimple subalgebras of the set Mn of n⇥n complex matrices, and P 2 M2n is a projection of rank n. We ... 
OFFDIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
(Elsevier, 20201215)Let n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥Aran P is said to be an offdiagonal corner of A, and L ... 
MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I
(Elsevier, 20210715)An algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all ... 
ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS
(American Mathematical Society, 20210720)We study the maximal algebraic degree of principal orthocompressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly ... 
OPERATORS WHICH ARE POLYNOMIALLY ISOMETRIC TO A NORMAL OPERATOR
(American Mathematical Society, 20200115)Let H be a complex, separable Hilbert space and B(H) denote the algebra of all bounded linear operators acting on H. Given a unitarilyinvariant norm k · ku on B(H) and two linear operators A and B in B(H), we shall say ... 
Normal operators with highly incompatible offdiagonal corners
(Polish Academy of Sciences, 20200525)Let H be a complex, separable Hilbert space, and B(H) denote the set of all bounded linear operators on H. Given an orthogonal projection P∈B(H) and an operator D∈B(H), we may write D=[D1D3D2D4] relative to the decomposition ... 
ParaHolomorphic Algebroids and ParaComplex Connections
(University of Waterloo, 20211217)The goal of this paper is to develop the theory of Courant algebroids with integrable paraHermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold ... 
Exact Formulas for Averages of Secular Coefficients
(University of Waterloo, 20210929)We study averages of secular coefficients that frequently appear in random matrix theory. We obtain exact formulas, identities and new asymptotics for these integrals as well as a technique to deal with singularities that ... 
A guide to Fautomatic sets
(University of Waterloo, 20210908)A selfcontained introduction to the theory of Fautomatic sets is given. Building on [Bell, Moosa, Fsets and finite automata, Journal de théorie des nombres de Bordeaux, 2019], contributions are made to both the foundations ... 
Applications of the minimal modelprogram in arithmetic dynamics
(University of Waterloo, 20210907)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 pullback action on divisors. ... 
Deformation theory of nearly G₂structures and nearly G₂ instantons
(University of Waterloo, 20210830)We study two different deformation theory problems on manifolds with a nearly G₂structure. The first involves studying the deformation theory of nearly G₂ manifolds. These are seven dimensional manifolds admitting real ... 
On the structure of invertible elements in certain FourierStieltjes algebras
(University of Waterloo, 20210827)Let $G$ be a locally compact group. The FourierStieltjes and Fourier algebras, $B(G)$ and $A(G)$ are defined by Eymard to act as dual objects of the measure and group algebras, $M(G)$ and $L^1(G)$, in a sense generalizing ... 
Trisections of nonorientable 4manifolds
(University of Waterloo, 20210824)Broadly, this thesis is concerned with trying to understand 4manifolds through 3dimensional techniques. From the point of view of smooth manifolds, dimension four is quite unique; one striking illustration of this is the ...