Now showing items 38-57 of 57

    • Plumbers' knots and unstable Vassiliev theory 

      Giusti, Chad David, 1978- (University of Oregon, 2010-06)
      We introduce a new finite-complexity knot theory, the theory of plumbers' knots, as a model for classical knot theory. The spaces of plumbers' curves admit a combinatorial cell structure, which we exploit to algorithmically ...
    • Primitive and Poisson spectra of non-semisimple twists of polynomial algebras 

      Brandl, Mary-Katherine, 1963- (University of Oregon, 2001)
      We examine a family of twists of the complex polynomial ring on n generators by a non-semisimple automorphism. In particular, we consider the case where the automorphism is represented by a single Jordan block. The ...
    • Probability on graphs: A comparison of sampling via random walks and a result for the reconstruction problem 

      Ahlquist, Blair, 1979- (University of Oregon, 2010-09)
      We compare the relaxation times of two random walks - the simple random walk and the metropolis walk - on an arbitrary finite multigraph G. We apply this result to the random graph with n vertices, where each edge is ...
    • Quantum Cluster Characters 

      Rupel, Dylan (University of Oregon, 2012)
      We de ne the quantum cluster character assigning an element of a quantum torus to each representation of a valued quiver (Q; d) and investigate its relationship to external and internal mutations of a quantum cluster ...
    • Representations of Hecke algebras and the Alexander polynomial 

      Black, Samson, 1979- (University of Oregon, 2010-06)
      We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the ...
    • Representations of Khovanov-Lauda-Rouquier algebras of affine Lie type 

      Muth, Robert (University of Oregon, 2016-10-27)
      We study representations of Khovanov-Lauda-Rouquier (KLR) algebras of affine Lie type. Associated to every convex preorder on the set of positive roots is a system of cuspidal modules for the KLR algebra. For a balanced ...
    • Representations of the Oriented Brauer Category 

      Reynolds, Andrew (University of Oregon, 2015-08-18)
      We study the representations of a certain specialization $\mathcal{OB}(\delta)$ of the oriented Brauer category in arbitrary characteristic $p$. We exhibit a triangular decomposition of $\mathcal{OB}(\delta)$, which we use ...
    • The RO(G)-graded Serre Spectral Sequence 

      Kronholm, William C., 1980- (University of Oregon, 2008-06)
      The theory of equivariant homology and cohomology was first created by Bredon in his 1967 paper and has since been developed and generalized by May, Lewis, Costenoble, and a host of others. However, there has been a notable ...
    • Semisimplicity of Certain Representation Categories 

      Foster, John (University of Oregon, 2013-10-03)
      We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence ...
    • Solvable Particle Models Related to the Beta-Ensemble 

      Shum, Christopher (University of Oregon, 2013-10-03)
      For beta > 0, the beta-ensemble corresponds to the joint probability density on the real line proportional to prod_{n > m}^N abs{x_n - x_m}^beta prod_{n = 1}^N w(x_n) where w is the weight of the system. It has the ...
    • Stabilization of chromatic functors 

      Leeman, Aaron, 1974- (University of Oregon, 2009-06)
      We study the Bousfield localization functors known as [Special characters omitted], as described in [MahS]. In particular we would like to understand how they interact with suspension and how they stabilize. We prove ...
    • Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder 

      Wade, Jeremy, 1981- (University of Oregon, 2009-06)
      We investigate Cesàro summability of the Fourier orthogonal expansion of functions on B d × I m , where B d is the closed unit ball in [Special characters omitted] and I m is the m -fold Cartesian product of the ...
    • A Super Version of Zhu's Theorem 

      Jordan, Alex, 1979- (University of Oregon, 2008-06)
      We generalize a theorem of Zhu relating the trace of certain vertex algebra representations and modular invariants to the arena of vertex super algebras. The theorem explains why the space of simple characters for the ...
    • The Einstein Constraint Equations on Asymptotically Euclidean Manifolds 

      Dilts, James (University of Oregon, 2015-08-18)
      In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz ...
    • The Geometry of quasi-Sasaki Manifolds 

      Welly, Adam (University of Oregon, 2016-10-27)
      Let (M,g) be a quasi-Sasaki manifold with Reeb vector field xi. Our goal is to understand the structure of M when g is an Einstein metric. Assuming that the S^1 action induced by xi is locally free or assuming a certain ...
    • The Homotopy Calculus of Categories and Graphs 

      Vicinsky, Deborah (University of Oregon, 2015-08-18)
      We construct categories of spectra for two model categories. The first is the category of small categories with the canonical model structure, and the second is the category of directed graphs with the Bisson-Tsemo model ...
    • Topics in Random Walks 

      Montgomery, Aaron (University of Oregon, 2013-10-03)
      We study a family of random walks defined on certain Euclidean lattices that are related to incidence matrices of balanced incomplete block designs. We estimate the return probability of these random walks and use it to ...
    • The Tracial Rokhlin Property for Countable Discrete Amenable Group Actions on Nuclear Tracially Approximately Divisible C*-Algebras 

      Sun, Michael (University of Oregon, 2014-09-29)
      In this dissertation we explore the question of existence of a property of group actions on C*-algebras known as the tracial Rokhlin property. We prove existence of the property in a very general setting as well as specialise ...
    • Uniqueness of Conformal Ricci Flow and Backward Ricci Flow on Homogeneous 4-Manifolds 

      Bell, Thomas (University of Oregon, 2013-10-03)
      In the first chapter we consider the question of uniqueness of conformal Ricci flow. We use an energy functional associated with this flow along closed manifolds with a metric of constant negative scalar curvature. Given ...
    • Zonotopes and Hypertoric Varieties 

      Arbo, Matthew (University of Oregon, 2016-02-23)
      Hypertoric varieties are a class of conical symplectic resolutions which are very computable. In the current literature, they are only defined constructively, using hyperplane arrangements. We provide an abstract definition ...