• PSEUDO SYMMETRIC MULTIFUNCTORS: COHERENCE AND EXAMPLES 

  Manco, Diego (University of Oregon, 2024-08-07)

  Donald Yau introduced pseudo symmetric Cat-multifunctors and proved that Mandell's inverse K-theory multifunctor is stably equivalent to a pseudo symmetric one. We prove a coherence result for pseudo symmetric Cat-multifunctors ...
• Two Problems in Symmetric Tensor Categories 

  Czenky, Agustina (University of Oregon, 2024-08-07)

  Fix an algebraically closed field k of characteristic $p \geq 0$. A symmetric fusion category $\mathcal C$ over k is a fusion category endowed with a braiding $c_{X,Y}: X\otimes Y \to Y \otimes X$ such that $c_{Y,X}c_{X, ...
• The Squish Map and the SL_2 Double Dimer Model 

  Foster, Leigh (University of Oregon, 2024-08-07)

  A plane partition, whose 3D Young diagram is made of unit cubes, can be approximated by a “coarser” plane partition, made of cubes of side length 2. Indeed, there are two such approximations obtained by “rounding up” or ...
• Visual Aspects of Gaussian Periods and Analogues 

  Platt, Samantha (University of Oregon, 2024-08-07)

  In this dissertation, we study Gaussian periods and their analogues from a visual perspective. Building on the work of Duke, Garcia, Hyde, Lutz, and others [BBF+14, BBGG+13, DGL15, GHL15], we introduce a more dynamical ...
• Hermitian Jacobi Forms of Higher Degree 

  Haight, Sean (University of Oregon, 2024-08-07)

  We develop the theory of Hermitian Jacobi forms in degree $n > 1$. This builds on the work of Klaus Haverkamp in \cite{HThesis} who developed this theory in degree $n = 1$. Haverkamp in turn generalized a monograph of ...
• Reducible Dehn Surgeries, Ribbon Concordance, and Satellite Knots 

  Bodish, Holt (University of Oregon, 2024-08-07)

  In this thesis we investigate knots and surfaces in $3$- and $4$-manifolds from the perspective of Heegaard Floer homology, knot Floer homology and Khovanov homology. We first investigate the \emph{Cabling Conjecture}, ...
• 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 ...

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