Now showing items 21-40 of 56

    • Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots 

      Pelatt, Kristine (University of Oregon, 2012)
      We produce explicit geometric representatives of non-trivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live ...
    • GKZ Hypergeometric Systems and Projective Modules in Hypertoric Category O 

      Hilburn, Justin (University of Oregon, 2016-10-27)
      In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fand-Ka ...
    • Gluing Bridgeland's stability conditions and Z2-equivariant sheaves on curves 

      Collins, John, 1981- (University of Oregon, 2009-06)
      We define and study a gluing procedure for Bridgeland stability conditions in the situation where a triangulated category has a semiorthogonal decomposition. As one application, we construct an open, contractible subset U ...
    • Graded representation theory of Hecke algebras 

      Nash, David A., 1982- (University of Oregon, 2010-06)
      We study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to ...
    • Group Actions on Hyperplane Arrangements 

      Moseley, Daniel (University of Oregon, 2012)
      In this dissertation, we will look at two families of algebras with connections to hyperplane arrangements that admit actions of finite groups. One of the fundamental questions to ask is how these decompose into irreducible ...
    • Group decompositions, Jordan algebras, and algorithms for p-groups 

      Wilson, James B., 1980- (University of Oregon, 2008-06)
      Finite p -groups are studied using bilinear methods which lead to using nonassociative rings. There are three main results, two which apply only to p -groups and the third which applies to all groups. First, for finite ...
    • Infinite dimensional versions of the Schur-Horn theorem 

      Jasper, John, 1981- (University of Oregon, 2011-06)
      We characterize the diagonals of four classes of self-adjoint operators on infinite dimensional Hilbert spaces. These results are motivated by the classical Schur-Horn theorem, which characterizes the diagonals of self-adjoint ...
    • Koszul and generalized Koszul properties for noncommutative graded algebras 

      Phan, Christopher Lee, 1980- (University of Oregon, 2009-06)
      We investigate some homological properties of graded algebras. If A is an R -algebra, then E (A) := Ext A ( R, R ) is an R-algebra under the cup product and is called the Yoneda algebra. (In most cases, we assume R ...
    • Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds 

      Perlmutter, Nathan (University of Oregon, 2015-08-18)
      Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are ...
    • 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 ...
    • 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 ...
    • 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 ...