Browsing Pure Mathematics by Title
Now showing items 36-55 of 165
-
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 ... -
Dispersing representations of semi-simple subalgebras of complex matrices
(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 ... -
Divisibility of Discriminants of Homogeneous Polynomials
(University of Waterloo, 2023-08-28)We prove several square-divisibility results about the discriminant of homogeneous polynomials of arbitrary degree and number of variables, when certain coefficients vanish, and give characterizations for when the discriminant ... -
The Eberlein Compactification of Locally Compact Groups
(University of Waterloo, 2013-01-24)A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection ... -
Elliptic Curves over Finite Fields and their l-Torsion Galois Representations
(University of Waterloo, 2015-09-08)Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ... -
The Enigma History and Mathematics
(University of Waterloo, 2016-10-25)In this thesis we look at the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, ... -
Equality of Number-Theoretic Functions over Consecutive Integers
(University of Waterloo, 2009-04-30)This thesis will survey a group of problems related to certain number-theoretic functions. In particular, for said functions, these problems take the form of when and how often they are equal over consecutive integers, n ... -
Exact C*-algebras and the Kirchberg-Phillips Nuclear Embedding Theorem
(University of Waterloo, 2019-08-08)A C*-algebra A is exact if the functor A ⊗ min (·) preserves short exact sequences. This is equivalent to the algebra A having a nuclear faithful *-representation. Exact C*-algebras are a class of C*-algebras which is ... -
Exact Formulas for Averages of Secular Coefficients
(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 ... -
Exactness and Noncommutative Convexity
(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 ... -
Existence and uniqueness of weak homotopy moment maps
(Elsevier, 2018-09-01)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 ... -
Exotic Group C*-algebras, Tensor Products, and Related Constructions
(University of Waterloo, 2016-06-15)Recently there has been a rejuvenated interest in exotic group C*-algebras, i.e., group C*-algebras which are "intermediate" to the full and reduced group C*-algebras. This resurgence began with the introduction of the ... -
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 ...