Now showing items 1-20 of 57

    • Cohomology of the Orlik-Solomon algebras 

      Pearson, Kelly Jeanne, 1970- (2000)
      The Orlik-Solomon algebra of a hyperplane arrangement first appeared from the Brieskorn and Orlik-Solomon theorems as the cohomology of the complement of this arrangement (if the ground field is complex). Later, it was ...
    • 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 ...
    • 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 ...
    • A Super Version of Zhu's Theorem 

      Jordan, Alex, 1979- (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 ...
    • 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 ...
    • 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 ...
    • Crossed product C*-algebras by finite group actions with a generalized tracial Rokhlin property 

      Archey, Dawn Elizabeth, 1979- (University of Oregon, 2008-06)
      This dissertation consists of two related parts. In the first portion we use the tracial Rokhlin property for actions of a finite group G on stably finite simple unital C *-algebras containing enough projections. The ...
    • Stabilization of chromatic functors 

      Leeman, Aaron, 1974- (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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder 

      Wade, Jeremy, 1981- (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 ...
    • 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 ...
    • 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 ...
    • Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus 

      Sun, Wei, 1979- (University of Oregon, 2010-06)
      This dissertation is a study of the relationship between minimal dynamical systems on the product of the Cantor set ( X ) and torus ([Special characters omitted]) and their corresponding crossed product C *-algebras. For ...
    • Blocks in Deligne's category Rep(St) 

      Comes, Jonathan, 1981- (University of Oregon, 2010-06)
      We give an exposition of Deligne's tensor category Rep(St) where t is not necessarily an integer. Thereafter, we give a complete description of the blocks in Rep(St) for arbitrary t. Finally, we use our result on blocks ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Crossed product C*-algebras of certain non-simple C*-algebras and the tracial quasi-Rokhlin property 

      Buck, Julian Michael, 1982- (University of Oregon, 2010-06)
      This dissertation consists of four principal parts. In the first, we introduce the tracial quasi-Rokhlin property for an automorphism α of a C *-algebra A (which is not assumed to be simple or to contain any projections). ...