• Exactness and Noncommutative Convexity 

  Manor, Nicholas (University of Waterloo, 2022-09-02)

  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 

  Humeniuk, Adam (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 ...

• Tracial and ideal structure of crossed products and related constructions 

  Ursu, Dan (University of Waterloo, 2022-08-17)

  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 Wilf-Zeilberger Problem 

  Sun, Yuxuan (University of Waterloo, 2022-08-15)

  In this paper, we give an algorithmic solution to a dynamical analog of the problem of certifying combinatorial identities by Wilf-Zeilberger pairs. Given two sequences generated in a dynamical setting, we calculate an ...

• Integrality theorems for symmetric instantons 

  Whitehead, Spencer (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 ...

• On Amenability Properties and Coideals of Quantum Groups 

  Anderson-Sackaney, Benjamin (University of Waterloo, 2022-07-27)

  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 non-commutative probability, and relations between them 

  Perales, Daniel (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 ...

• Dispersing representations of semi-simple subalgebras of complex matrices 

  Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 2022-06-01)

  In this paper we consider the problem of determining the maximum dimension of P?(A!B)P, where A and B are unital, semi-simple subalgebras of the set Mn of n⇥n complex matrices, and P 2 M2n is a projection of rank n. We ...

• OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn) 

  Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 2020-12-15)

  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 ⊥A|ran P is said to be an off-diagonal corner of A, and L ...

• MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I 

  Cramer, Zachary; Marcoux, Laurent W.; Radjavi, Heydar (Elsevier, 2021-07-15)

  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 

  Bernik, Janez; Livshits, Leo; MacDonald, Gordon W.; Marcoux, Laurent W.; Mastnak, Mitja; Radjavi, Heydar (American Mathematical Society, 2021-07-20)

  We study the maximal algebraic degree of principal ortho-compressions 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 

  Marcoux, Laurent W.; Zhang, Yuanhang (American Mathematical Society, 2020-01-15)

  Let H be a complex, separable Hilbert space and B(H) denote the algebra of all bounded linear operators acting on H. Given a unitarily-invariant norm k · ku on B(H) and two linear operators A and B in B(H), we shall say ...

• Normal operators with highly incompatible off-diagonal corners 

  Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Polish Academy of Sciences, 2020-05-25)

  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 ...

• Para-Holomorphic Algebroids and Para-Complex Connections 

  Patterson, Aidan (University of Waterloo, 2021-12-17)

  The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian 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 

  Medjedovic, Andean (University of Waterloo, 2021-09-29)

  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 F-automatic sets 

  Hawthorne, Christopher (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 ...

• Applications of the minimal modelprogram in arithmetic dynamics 

  Nasserden, Brett (University of Waterloo, 2021-09-07)

  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 pull-back action on divisors. ...

• Deformation theory of nearly G₂-structures and nearly G₂ instantons 

  Singhal, Ragini (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 ...

• On the structure of invertible elements in certain Fourier-Stieltjes algebras 

  Thamizhazhagan, Aasaimani (University of Waterloo, 2021-08-27)

  Let $G$ be a locally compact group. The Fourier-Stieltjes 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 non-orientable 4-manifolds 

  Naylor, Patrick (University of Waterloo, 2021-08-24)

  Broadly, this thesis is concerned with trying to understand 4-manifolds through 3-dimensional techniques. From the point of view of smooth manifolds, dimension four is quite unique; one striking illustration of this is the ...

View more