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Browsing Mathematics Theses and Dissertations by Title
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Now showing items 88-107 of 125
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(University of Oregon, 2024-01-09)In this study, we focus on two topics in classical number theory. First, we examine Thue equations—equations of the form F(x, y) = h where F(x, y) is an irreducible, integral binary form and h is an integer—and we give ...
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(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 ...
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(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 ...
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(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 ...
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(University of Oregon, 2019-09-18)In this thesis, we prove regularity theory for nonlinear fourth order and second order elliptic equations. First, we show that for a certain class of fourth order equations in the double divergence form, where the nonlinearity ...
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(University of Oregon, 2017-09-06)For each finite dimensional Lie algebra $\mathfrak{g}$ and positive integer $k$ there exists a modular tensor category $\mathcal{C}(\mathfrak{g},k)$ consisting of highest weight integrable $\hat{\mathfrak{g}}$-modules of ...
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(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 ...
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(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 ...
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(University of Oregon, 2023-07-06)We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by ...
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(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 ...
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(University of Oregon, 2024-01-09)We study properties of surfaces embedded in 4-manifolds by way of HeegaardFloer homology. We begin by showing link Floer homology obstructs concordance through ribbon homology cobordisms; this extends the work of Zemke ...
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(University of Oregon, 2018-09-06)We compute the RO(C2)-graded Bredon cohomology of certain families of real and complex C2-equivariant Grassmannians.
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(University of Oregon, 2022-10-04)Let $p$ be an odd prime, and let $C_p$ denote the cyclic group of order $p$. We use equivariant surgery methods to classify all closed, connected $2$-manifolds with an action of $C_p$. We then use this classification in ...
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(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 ...
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(University of Oregon, 2024-01-10)In 1992, Stolz proved that, among simply connected Spin-manifolds of dimension5 or greater, the vanishing of a particular invariant α is necessary and sufficient for the existence of a metric of positive scalar curvature. ...
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(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 ...
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(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 ...
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(University of Oregon, 2020-09-24)We give an explicit description of the category of Yoneda extensions of standard modules over KLR algebras for two special cases in Lie type A. In these two special cases, the A-infinity category structure of the Yoneda ...
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(University of Oregon, 2018-09-06)We prove a nonpolarized analogue of the asymptotic characterization of T<sup>2</sup>-symmetric Einstein flow solutions completed recently by LeFloch and Smulevici. We impose a far weaker condition, but obtain identical ...
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(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 ...
Now showing items 88-107 of 125