This collection contains some of the theses and dissertations produced by students in the University of Oregon Mathematics Graduate Program. Paper copies of these and other dissertations and theses are available through the UO Libraries.
In 1992, Stolz proved that, among simply connected Spin-manifolds of dimension5 or greater, the vanishing of a particular invariant α is necessary and sufficient
for the existence of a metric of positive scalar curvature. ...
Delfin Ares de Parga, Alonso(University of Oregon, 2024-01-10)
This dissertation initiates the study of $L^p$-modules, which are modules over $L^p$-operator algebras inspired by Hilbert modules over C*-algebras. The primary motivation for studying $L^p$-modules is to explore the ...
Let $L$ be a link in a thickened annulus. In [GLW17], Grigsby-Licata-Wehrli showed that the annular Khovanov homology of $L$ is equipped with an action of $\exsltwo$, the exterior current algebra of the Lie algebra $\sltwo$. ...
We study properties of surfaces embedded in 4-manifolds by way of HeegaardFloer homology. We begin by showing link Floer homology obstructs concordance
through ribbon homology cobordisms; this extends the work of Zemke ...
In this paper, we build on the work of Lipshitz, Ozsv\'{a}th, and Thurston by constructing an algorithm that generates a weighted $A_\infty$-diagonal given a family of contractions of the weighted associahedron complexes. ...
In this study, we focus on two topics in classical number theory. First, we examine Thue equations—equations of the form F(x, y) = h where F(x, y) is an irreducible, integral binary form and h is an integer—and we give ...
This thesis describes the Fano scheme $F(Y)$ of lines on a general cubic threefold $Y$ containing a plane over a field $k$ of characteristic different from $2$. One irreducible component of $F(Y)$ is birational (over $k$) ...
Graphs and matroids are two of the most important objects in combinatorics.We study invariants of graphs and matroids that behave well with respect to
certain morphisms by realizing these invariants as functors from a ...
This dissertation has two main topics. The first is the introduction and in-depth study of a new poset theoretic structure designed to help us better understand the notion of lexicographic shellability of partially ordered ...
In the unstable range, topological vector bundles over finite CW complexes are difficult to classify in general. Over complex projective spaces \mathbb{C}P^n, such bundles are far from being fully classified, or even ...
We provide a framework for analyzing the geometry and topology of the canonical polyhedral complex of ReLU neural networks, which naturally divides the input space into linear regions. Beginning with a category appropriate ...
We study the relationship between the algebra of module homomorphisms under composition and 4-dimensional cobordisms in the context of bordered Heegaard Floer homology. In particular, we prove that composition of module ...
Hendrickson, Allan(University of Oregon, 2024-01-09)
We consider the problem of dimension growth in AH algebras $A$ defined as inductive limits $A = \lim_{n \to \infty} (M_{R_n}(C(X_n)),\phi_{n})$ over finite connected CW-complexes $X_n$. We show that given any sequence ...
Manis, Merle Eugene(University of Oregon, 1966-06)
The purpose of this paper is to extend some results
from the theory of valuations on a field to an arbitrary
commutative ring with identity. The results obtained are
well known when interpreted in the context of a field ...
We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by ...
Let $C_l$ denote the cyclic group of prime order $l$ and let $k$ be a field. We define a Mackey $\underline{k}$-algebra $\underline{k}[x_\theta]$ which is constructed by adjoining a free commutative variable to the free ...
We explore generalized Mahler measures associated to regions in the complex plane. These generalized Mahler measures describe the complexity of polynomials in C[x] by comparing the geometry of their roots to subsets of C. ...
We construct differential operators acting on overconvergent Hilbert modular forms. This extends work of Katz in the case of p-adic Hilbert modular forms, and of Harron--Xiao and Liu for overconvergent Siegel modular forms. ...
We define a useful diagram for studying fixed-point-free involution words. Following the example of Little, we define a specific and a general bumping algorithm on these diagrams. These algorithms serve as the basis for ...