Now showing items 28-47 of 57

• #### 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 ...
• #### On Algebras Associated to Finite Ranked Posets and Combinatorial Topology: The Koszul, Numerically Koszul and Cohen-Macaulay Properties ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### Representations of Hecke algebras and the Alexander polynomial ﻿

(University of Oregon, 2010-06)
We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the ...
• #### Representations of Khovanov-Lauda-Rouquier algebras of affine Lie type ﻿

(University of Oregon, 2016-10-27)
We study representations of Khovanov-Lauda-Rouquier (KLR) algebras of affine Lie type. Associated to every convex preorder on the set of positive roots is a system of cuspidal modules for the KLR algebra. For a balanced ...
• #### Representations of the Oriented Brauer Category ﻿

(University of Oregon, 2015-08-18)
We study the representations of a certain specialization $\mathcal{OB}(\delta)$ of the oriented Brauer category in arbitrary characteristic $p$. We exhibit a triangular decomposition of $\mathcal{OB}(\delta)$, which we use ...
• #### The RO(G)-graded Serre Spectral Sequence ﻿

(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 ...
• #### Semisimplicity of Certain Representation Categories ﻿

(University of Oregon, 2013-10-03)
We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence ...
• #### Solvable Particle Models Related to the Beta-Ensemble ﻿

(University of Oregon, 2013-10-03)
For beta > 0, the beta-ensemble corresponds to the joint probability density on the real line proportional to prod_{n > m}^N abs{x_n - x_m}^beta prod_{n = 1}^N w(x_n) where w is the weight of the system. It has the ...