• A SPECIAL ENDOMORPHISM OF THE STANDARD GAITSGORY CENTRAL OBJECT OF THE AFFINE HECKE CATEGORY 

  Hathaway, Jay (University of Oregon, 2024-03-25)

  Using the combinatorial description of the standard Gaitsgory centralobject of the (extended, graded) affine type A Hecke category due to Elias, we show the existence of and explicitly describe the unique endomorphism that ...
• Scalar Curvature and Transfer Maps in Spin and Spin^c Bordism 

  Granath, Elliot (University of Oregon, 2024-01-10)

  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. ...
• C*-Correspondences, Hilbert Bimodules, and their L^p Versions 

  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 ...
• Structures and Computations in Annular Khovanov Homology 

  Davis, Champ (University of Oregon, 2024-01-09)

  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 $\sltwo$. ...
• Ribbons, Satellites, and Exotic Phenomena in Heegaard Floer Homology 

  Guth, Gary (University of Oregon, 2024-01-09)

  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 ...
• New A-infinity Diagonals from Contractions of the Weighted Associahedra 

  Phillips, Bo (University of Oregon, 2024-01-09)

  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. ...
• Polynomial Root Distribution and Its Impact on Solutions to Thue Equations 

  Knapp, Greg (University of Oregon, 2024-01-09)

  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 ...
• Lines on Cubic Threefolds and Fourfolds Containing a Plane 

  Brooke, Corey (University of Oregon, 2024-01-09)

  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 $k$) ...
• Categorical Invariants of Graphs and Matroids 

  Miyata, Dane (University of Oregon, 2024-01-09)

  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 ...
• A Partial Order Structure on the Shellings of Lexicographically Shellable Posets. 

  Lacina, Stephen (University of Oregon, 2024-01-09)

  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 ...
• Metastable Complex Vector Bundles over Complex Projective Spaces 

  Hu, Yang (University of Oregon, 2024-01-09)

  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 ...
• Accessing the Topological Properties of Neural Network Functions. 

  Masden, Marissa (University of Oregon, 2024-01-09)

  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 ...
• Composition and Cobordism Maps 

  Cohen, Jesse (University of Oregon, 2024-01-09)

  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 ...
• Non-Z-Stable Simple AH Algebras 

  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 ...
• An Approach to the Irreducible Representations of Finite Groups of Lie Type Through Block Theory and Special Conjugacy Classes 

  Boyce, Richard Alan (University of Oregon, 1980-08)
• Valuations on a Commutative Ring 

  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 ...
• Representations of Partition Categories 

  Vargas, Max (University of Oregon, 2023-07-06)

  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 ...
• Homological Algebra for Polynomial Mackey Rings over Prime Cyclic Groups 

  Casebolt, Ross (University of Oregon, 2022-10-26)

  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 ...
• The Distribution of the Cusped Hypocycloidal Mahler Measure 

  Hunter, Nathan (University of Oregon, 2022-10-26)

  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. ...
• Families of Differential Operators Acting on Overconvergent Hilbert Modular Forms 

  Aycock, Jon (University of Oregon, 2022-10-26)

  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. ...

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