Now showing items 35-54 of 64

    • Manifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvalues 

      Zhang, Tan, 1969- (University of Oregon, 2000)
      Relative to a non-degenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skew-symmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant ...
    • Metrics of positive scalar curvature and generalised Morse functions 

      Walsh, Mark, 1976- (University of Oregon, 2009-06)
      We study the topology of the space of metrics of positive scalar curvature on a compact manifold. The main tool we use for constructing such metrics is the surgery technique of Gromov and Lawson. We extend this technique ...
    • Motives of Log Schemes 

      Howell, Nicholas (University of Oregon, 2017-09-06)
      This thesis introduces two notions of motive associated to a log scheme. We introduce a category of log motives à la Voevodsky, and prove that the embedding of Voevodsky motives is an equivalence, in particular proving ...
    • Motivic Integral of K3 Surfaces over a Non-Archimedean Field 

      Stewart, Allen (University of Oregon, 2014-09-29)
      We prove a formula expressing the motivic integral of a K3 surface over C((t)) with semi-stable reduction in terms of the associated limit mixed Hodge structure. Secondly, for every smooth variety over a complete discrete ...
    • Multinets in P^2 and P^3 

      Bartz, Jeremiah (University of Oregon, 2013-10-03)
      In this dissertation, a method for producing multinets from a net in P^3 is presented. Multinets play an important role in the study of resonance varieties of the complement of a complex hyperplane arrangement and very few ...
    • Multiplier Theorems on Anisotropic Hardy Spaces 

      Wang, Li-An (University of Oregon, 2012)
      We extend the theory of singular integral operators and multiplier theorems to the setting of anisotropic Hardy spaces. We first develop the theory of singular integral operators of convolution type in the anisotropic ...
    • Non-existence of a stable homotopy category for p-complete abelian groups 

      Vanderpool, Ruth, 1980- (University of Oregon, 2009-06)
      We investigate the existence of a stable homotopy category (SHC) associated to the category of p -complete abelian groups [Special characters omitted]. First we examine [Special characters omitted] and prove [Special ...
    • On Algebras Associated to Finite Ranked Posets and Combinatorial Topology: The Koszul, Numerically Koszul and Cohen-Macaulay Properties 

      Kloefkorn, Tyler (University of Oregon, 2014-09-29)
      This dissertation studies new connections between combinatorial topology and homological algebra. To a finite ranked poset Γ we associate a finite-dimensional quadratic graded algebra RΓ. Assuming Γ satisfies a combinatorial ...
    • On the Subregular J-ring of Coxeter Systems 

      Xu, Tianyuan (University of Oregon, 2017-09-06)
      Let (W, S) be an arbitrary Coxeter system, and let J be the asymptotic Hecke algebra associated to (W, S) via Kazhdan-Lusztig polynomials by Lusztig. We study a subalgebra J_C of J corresponding to the subregular cell C ...
    • 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 ...
    • Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of Unity 

      Schopieray, Andrew (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 ...
    • 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 ...