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Filtering by: Creator Schnitzler, Christine E. Remove constraint Creator: Schnitzler, Christine E. Academic Affiliation Mathematics Remove constraint Academic Affiliation: Mathematics

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  • On the Structure of the Orbit Spaces of Almost Torus Manifolds with Non-negative Curvature

    Creator:
    Dong, Zheting
    Abstract:
    An almost torus manifold $M$ is a closed $(2n+1)$-dimensional orientable Riemannian manifold with an effective, isometric $n$-torus action such that the fixed point set $M^T$ is non-empty. Almost torus manifolds are analogues of torus manifolds in odd dimension and share many of the characteristics of torus manifolds. For example, both...
    Resource Type:
    Dissertation
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    orbit spaces of almost torus manifolds with non-negative curvature. Abstract approved: Christine M

  • The Horizon Measure: A New Look at Curvature

    Creator:
    Mills, Arthur M.
    Abstract:
    An important problem in computer graphics is to determine where contour lines and ridges appear in a surface constructed from a triangle mesh. In this presentation we will investigate a new answer to this problem – the horizon measure. The horizon measure determines the likelihood of contour lines to appear...
    Resource Type:
    Capstone Project
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    the first fundamental form E,F,G to be E(u0, v0) = 〈φu, φu〉p F (u0, v0) = 〈φu, φv〉p G(u0, v0) = 〈φv

  • The Eight Geometries of the Geometrization Conjecture

    Creator:
    Grady, Noella
    Abstract:
    In this paper we explore the eight geometries of Thurston's geometrization conjecture. We begin by discussing group actions, covering space topology, fiber bundles, and Seifert fiber spaces. We make precise the notion of a geometric structure. We then discuss the two dimensional geometries including a brief proof of the uniformization...
    Resource Type:
    Capstone Project
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    , and e ·m = m for e the identity element of G and all m ∈M . A right group action can be defined

  • Classifying seven dimensional manifolds of fixed cohomology type

    Creator:
    Montagantirud, Pongdate
    Abstract:
    Finding new examples of compact simply connected spaces admitting a Riemannian metric of positive sectional curvature is a fundamental problem in differential geometry. Likewise, studying topological properties of families of manifolds is very interesting to topologists. The Eschenburg spaces combine both of those interests: they are positively curved Riemannian manifolds...
    Resource Type:
    Dissertation
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    : Classifying Seven Dimensional Manifolds of Fixed Cohomology Type Abstract approved: Christine M. Escher

  • The cohomology rings of seven dimensional primitive cohomogeneity one manifolds

    Creator:
    Ultman, Shari K.
    Abstract:
    A striking feature in the study of Riemannian manifolds of positive sectional curvature is the narrowness of the collection of known examples. In this thesis, we examine the structure of the cohomology rings of three families of compact simply connected seven dimensional Riemannian manifolds that may contain new examples of...
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    Dissertation
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    Dimensional Primitive Cohomogeneity One Manifolds Abstract approved: Christine M. Escher A striking

  • Instability of Mapper Type Algorithms for Topological Data Analysis

    Creator:
    Wentland, Danial
    Abstract:
    Mapper is a tool designed by Gurjeet Singh, Facundo Mémoli, and Gunnar Carlsson for Topological Data Analysis (TDA) that constructs a simplicial complex from a finite subset of a metric space, which has been met with great success. Due to the many moving parts of Mapper and the potential it...
    Resource Type:
    Capstone Project
    Full Text:
    Analysis Danny Wentland Advisor: Professor Christine Escher Oregon State University May 2020 Contents 1

  • Explicit Dynamical Systems on the Sierpiński Curve

    Creator:
    Homsomboon, Worapan
    Resource Type:
    Dissertation
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    his guidance and encouragement. I also would like to thank all my committee members Prof. Christine

  • A thin codimension-one decomposition of the Hilbert Cube

    Creator:
    Phon-On, Aniruth
    Abstract:
    For cell-like upper semicontinuous(usc) decompositions G of finite dimensional manifolds M, the decomposition space M/G turns out to be an ANR provided M/G is finite dimensional ([Dav07], page 129 ). Furthermore, if M/G is finite dimensional and has the Disjoint Disks Property (DDP), then M/G is homeomorphic to M ([Dav07],...
    Resource Type:
    Dissertation
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    thanks to the members of my Graduate committee, Professors William A. Bogley, Mary Flahive, Christine

  • Algebraic Pappus Curves

    Creator:
    Hatase, Tatsuhiko
    Abstract:
    We show that Pappus Curves, introduced by R. Schwartz to study his dynamical system in the real projective plane generated by iterated applications of the classical Pappus Theorem, are algebraic exactly in the linear case. Our approach is to use properties of projective curves such as singular points, genus, number...
    Resource Type:
    Dissertation
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    projective transformation represented by a matrix T =  a b c d e f g h i  , then let AT

  • Shift dynamics for cyclically presented groups with length four positive relators

    Creator:
    Parker, Forrest W.
    Abstract:
    In 2014, W. Bogley identified a relation between the algebraic and geometric prop- erties of cyclically presented groups Gn (w) in the case where w = x0xkxl is a positive word of length three. Specifically, it was shown that the dynamics of the shift θG on the group G =...
    Resource Type:
    Dissertation
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    points for the shift always derive from finite cyclically presented subgroups. Theorem E The shift θG

  • The local conservation laws of the nonlinear Schrödinger equation

    Creator:
    Barrett, Johnner
    Abstract:
    The nonlinear Schrödinger equation is a well-known partial differential equation that provides a successful model in nonlinear optic theory, as well as other applications. In this dissertation, following a survey of mathematical literature, the geometric theory of differential equations is applied to the nonlinear Schrödinger equation. The main result of...
    Resource Type:
    Dissertation
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    ], which will be used here, is = -q.. + 2x 1q12 q, (1.1) where x E and q is a complex-valued probability

  • On the Topologies of Moduli Spaces of Polygons: A Taxonomic Approach

    Creator:
    Krughoff, Stephen A.
    Abstract:
    Consider a polygon lying in the Euclidean plane with labeled edge lengths. The moduli space of polygons is the space of all polygons with the same labeled edge lengths, modulo orientation preserving isometries. It is well known that this space is generically a smooth manifold. For certain combinations of edge...
    Resource Type:
    Dissertation
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    topology. To Dr. Christine Escher for teaching me the interaction between algebraic topology and geometry

  • On the Logical Independence of (DR) and (CLA)

    Creator:
    Birnbaum. Dionysus A.
    Abstract:
    In 1941, J.H.C. Whitehead posed the question of whether asphericity is a hereditary property for 2-dimensional CW complexes. This question remains unanswered, but has led to the development of several algebraic and topological properties that are sufficient (but not necessary) for the asphericity of presentation 2-complexes. While many of the...
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    Dissertation
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    this point. I would also like to thank my committee, Ren Guo and Christine Escher, who have always

  • Continued fractions and the divisor at infinity on a hyperelliptic curve : examples and order bounds

    Creator:
    Daowsud, Katthaleeya
    Abstract:
    We use the theory of continued fractions over function fields in the setting of hyperelliptic curves of equation y²=f(x), with deg(f)=2g+2. By introducing a new sequence of polynomials defined in terms of the partial quotients of the continued fraction expansion of y, we are able to bound the sum of...
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    Dissertation
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    to E. Artin [3]. Much more recently, Friesen in particular has studied the structure of class

  • A New Algorithm for Computing the Veech Group of a Translation Surface

    Creator:
    Edwards, Brandon
    Abstract:
    We give a new characterization of elements in the Veech group of a translation surface. This provides a computational test for Veech group membership. We use this computational test in an algorithm that detects when the Veech group is a lattice (has co-finite area), and in this case computes a...
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    Dissertation
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    singular base points y0 = Q 2 e⌃ and will be interested in focusing on the restriction of dev Q to a star

  • Splittings of skeletal homotopy modules

    Creator:
    Seaders, Nicole Sheree
    Abstract:
    This thesis is devoted to determining structure results on a group relative to a subgroup, using information about the kernel of the boundary map of associated free resolutions. If Y is a CW-complex with homotopy type K(G,1) then for n ≥ 2 the nth skeletal homotopy module, hn(Y ) =...
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    Dissertation
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    employment. I would like to extend special thanks to Tom Schmidt, Christine Escher, Mary Flahive, Ron

  • Rigidity of Vertex-Regular Actions on Fuchsian Buildings

    Creator:
    Smith, Samantha T.
    Abstract:
    We present a method by which torsion-free groups of automorphisms of a 2-dimensional hyperbolic building which act simply transitively on the vertex set can be constructed, and prove that any such group can be obtained by this construction. The method produces groups defined by finite presentations with strong small cancellation...
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    Dissertation
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    of the presentation 〈a, b, c, d, e | ab2ad, bc2be, cd2ca, de2db, ea2ec〉. To assemble the

  • The structure of E6

    Creator:
    Wangberg, Aaron D.
    Abstract:
    A fundamental question related to any Lie algebra is to know its subalgebras. This is particularly true in the case of E6, an algebra which seems just large enough to contain the algebras which describe the fundamental forces in the Standard Model of particle physics. In this situation, the question...
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    Dissertation
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    , referred to as multiplication, such that 1. ∃ e ∈ G such that x · e = x = e · x ∀x ∈ G 2. ∀x ∈ G, ∃x−1

  • Enumeration Problems on Symmetries of Riemann Surfaces

    Creator:
    Camacho, Charles A.
    Abstract:
    We describe two combinatorial problems in the theory of automorphism groups of compact Riemann surfaces of genus two or greater: enumerate the topological actions of a finite group on surfaces and determine the set of genera of surfaces admitting such a group action, called the genus spectrum. We illustrate results...
    Resource Type:
    Dissertation
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    stages of my research; and Christine Escher for supportive feedback. I would like to acknowledge the

  • Representations of fractional Brownian motion

    Creator:
    Wichitsongkram, Noppadon
    Abstract:
    Integral representations provide a useful framework of study and simulation of fractional Browian motion, which has been used in modeling of many natural situations. In this thesis we extend an integral representation of fractional Brownian motion that is supported on a bounded interval of ℝ to integral representation that is...
    Resource Type:
    Dissertation
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    : Mina E. Ossiander Integral representations provide a useful framework of study and simulation of