Browsing Pure Mathematics by Type "Master Thesis"
Now showing items 1-20 of 65
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Abstract and Explicit Constructions of Jacobian Varieties
(University of Waterloo, 2018-08-10)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 ... -
Algebraic characterization of multivariable dynamics
(University of Waterloo, 2009-03-26)Let X be a locally compact Hausdorff space along with n proper continuous maps σ = (σ1 , · · · , σn ). Then the pair (X, σ) is called a dynamical system. To each system one can associate a universal operator algebra called ... -
The Algebraic Kirchberg--Phillips Conjecture for Leavitt Path Algebras
(University of Waterloo, 2015-09-18)This essay is meant to be an exposition of the theory of Leavitt path algebras and graph C*-algebras, with an aim to discuss some current classification questions. These two classes of algebras sit on opposite sides of a ... -
Amenability for the Fourier Algebra
(University of Waterloo, 2007-08-29)The Fourier algebra A(G) can be viewed as a dual object for the group G and, in turn, for the group algebra L1(G). It is a commutative Banach algebra constructed using the representation theory of the group, and from which ... -
Artin's Conjecture: Unconditional Approach and Elliptic Analogue
(University of Waterloo, 2008-08-11)In this thesis, I have explored the different approaches towards proving Artin's `primitive root' conjecture unconditionally and the elliptic curve analogue of the same. This conjecture was posed by E. Artin in the year ... -
Artin's Primitive Root Conjecture and its Extension to Compositie Moduli
(University of Waterloo, 2008-08-11)If we fix an integer a not equal to -1 and which is not a perfect square, we are interested in estimating the quantity N_{a}(x) representing the number of prime integers p up to x such that a is a generator of the cyclic ... -
Asymptotic Distributions for Block Statistics on Non-crossing Partitions
(University of Waterloo, 2014-01-23)The set of non-crossing partitions was first studied by Kreweras in 1972 and was known to play an important role in combinatorics, geometric group theory, and free probability. In particular, it has a natural embedding ... -
Branched Covering Constructions and the Symplectic Geography Problem
(University of Waterloo, 2008-08-15)We apply branched covering techniques to construct minimal simply-connected symplectic 4-manifolds with small χ_h values. We also use these constructions to provide an alternate proof that for each s ≥ 0, there exists a ... -
Classical Field Theory in the BV Formalism
(University of Waterloo, 2016-09-20)This document is a review of the perspective on classical eld theories presented in [2] and [3]. -
Counting points of bounded height on del Pezzo surfaces
(University of Waterloo, 2006)del Pezzo surfaces are isomorphic to either P<sup>1</sup> x P<sup>1</sup> or P<sup>2</sup> blown up <i>a</i> times, where <i>a</i> ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P<sup>2</sup> ... -
Degree Spectra of Unary relations on ω and ζ
(University of Waterloo, 2009-08-13)Let X be a unary relation on the domain of (ω,<). The degree spectrum of X on (ω,<) is the set of Turing degrees of the image of X in all computable presentations of (ω,<). Many results are known about the types of degree ... -
Derived Geometry and the Integrability Problem for G-Structures
(University of Waterloo, 2017-08-24)In this thesis, we study the integrability problem for G-structures. Broadly speaking, this is the problem of determining topological obstructions to the existence of principal G-subbundles of the frame bundle of a manifold, ... -
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 ... -
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 ... -
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 ...