Browsing Mathematics Theses and Dissertations by Issue Date
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Cohomology of the OrlikSolomon algebras
(2000)The OrlikSolomon algebra of a hyperplane arrangement first appeared from the Brieskorn and OrlikSolomon theorems as the cohomology of the complement of this arrangement (if the ground field is complex). Later, it was ... 
Manifolds with indefinite metrics whose skewsymmetric curvature operator has constant eigenvalues
(University of Oregon, 2000)Relative to a nondegenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skewsymmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant ... 
Primitive and Poisson spectra of nonsemisimple twists of polynomial algebras
(University of Oregon, 2001)We examine a family of twists of the complex polynomial ring on n generators by a nonsemisimple automorphism. In particular, we consider the case where the automorphism is represented by a single Jordan block. The ... 
The RO(G)graded Serre Spectral Sequence
(University of Oregon, 200806)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 ... 
Group decompositions, Jordan algebras, and algorithms for pgroups
(University of Oregon, 200806)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 ... 
A Super Version of Zhu's Theorem
(University of Oregon, 200806)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 ... 
Crossed product C*algebras by finite group actions with a generalized tracial Rokhlin property
(University of Oregon, 200806)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 ... 
Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder
(University of Oregon, 200906)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 ... 
Stabilization of chromatic functors
(University of Oregon, 200906)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 Walgebras of classical type
(University of Oregon, 200906)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 Z2equivariant sheaves on curves
(University of Oregon, 200906)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 ... 
Nonexistence of a stable homotopy category for pcomplete abelian groups
(University of Oregon, 200906)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 ... 
Metrics of positive scalar curvature and generalised Morse functions
(University of Oregon, 200906)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
(University of Oregon, 200906)We investigate some homological properties of graded algebras. If A is an R algebra, then E (A) := Ext A ( R, R ) is an Ralgebra under the cup product and is called the Yoneda algebra. (In most cases, we assume R ... 
The crossed product of C(X) by a free minimal action of R
(University of Oregon, 201006)In this dissertation, we will study the crossed product C*algebras obtained from free and minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. We first define stable ... 
Blocks in Deligne's category Rep(St)
(University of Oregon, 201006)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
(University of Oregon, 201006)We study the graded representation theory of the IwahoriHecke 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 selfintersection local time for a superprocess over a stochastic flow
(University of Oregon, 201006)This dissertation examines the existence of the selfintersection 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
(University of Oregon, 201006)We introduce a new finitecomplexity 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 minimal dynamical systems on the product of the Cantor set and the torus
(University of Oregon, 201006)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 ...