Now showing items 16-35 of 56

• #### Dancing in the Stars: Topology of Non-k-equal Configuration Spaces of Graphs ﻿

(University of Oregon, 2016-11-21)
We prove that the non-k-equal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit ...
• #### Finite W-algebras of classical type ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...