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Browsing Mathematics Theses and Dissertations by Title
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Now showing items 91-110 of 125
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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 ...
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(University of Oregon, 2024-01-09)Let $L$ be a link in a thickened annulus. In [GLW17], Grigsby-Licata-Wehrli showed that the annular Khovanov homology of $L$ is equipped with an action of $\exsltwo$, the exterior current algebra of the Lie algebra $\sltwo$. ...
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(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 ...
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(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 ...
Now showing items 91-110 of 125