Now showing items 18-37 of 64

    • Equivariant Derived Categories Associated to a Sum of Potentials 

      Lim, Bronson (University of Oregon, 2017-09-06)
      We construct a semi-orthogonal decomposition for the equivariant derived category of a hypersurface associated to the sum of two potentials. More specifically, if $f,g$ are two homogeneous poynomials of degree $d$ defining ...
    • Faithful tropicalization of hypertoric varieties 

      Kutler, Max (University of Oregon, 2017-09-06)
      The hypertoric variety M_A defined by an arrangement A of affine hyperplanes admits a natural tropicalization, induced by its embedding in a Lawrence toric variety. In this thesis, we explicitly describe the polyhedral ...
    • Finite W-algebras of classical type 

      Brown, Jonathan, 1975- (University of Oregon, 2009-06)
      In this work we prove that the finite W -algebras associated to nilpotent elements in the symplectic or orthogonal Lie algebras whose Jordan blocks are all the same size are quotients of twisted Yangians. We use this to ...
    • Frames Generated by Actions of Locally Compact Groups 

      Iverson, Joseph (University of Oregon, 2016-10-27)
      Let $G$ be a second countable, locally compact group which is either compact or abelian, and let $\rho$ be a unitary representation of $G$ on a separable Hilbert space $\mathcal{H}_\rho$. We examine frames of the form $\{ ...
    • Generalized Near-Group Categories 

      Thornton, Josiah (University of Oregon, 2012)
      We give an exposition of near-group categories and generalized near-group categories. We show that both have a pseudounitary structure. We complete the classification of braided near-group categories and discuss the inherent ...
    • Generalized self-intersection local time for a superprocess over a stochastic flow 

      Heuser, Aaron, 1978- (University of Oregon, 2010-06)
      This dissertation examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions d ≤ 3, which through constructive methods, gives a Tanaka like representation. The ...
    • 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 ...
    • Gluing manifolds with boundary and bordisms of positive scalar curvature metrics 

      Kazaras, Demetre (University of Oregon, 2017-09-06)
      This thesis presents two main results on analytic and topological aspects of scalar curvature. The first is a gluing theorem for scalar-flat manifolds with vanishing mean curvature on the boundary. Our methods involve tools ...
    • 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 ...
    • Homological Properties of Standard KLR Modules 

      Steinberg, David (University of Oregon, 2017-05-01)
      Khovanov-Lauda-Rouquier algebras, or KLR algebras, are a family of algebras known to categorify the upper half of the quantized enveloping algebra of a given Lie algebra. In finite type, these algebras come with a family ...
    • 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 ...
    • 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 ...