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  • A Characterization of Anisotropic H^1(R^N) by Smooth Homogeneous Multipliers 
    Hiserote, Martin (University of Oregon, 2019-09-18)
    We extend a well known result of Uchiyama, which gives a sufficient condition for a family of smooth homogeneous multipliers to characterize the Hardy space H^1(R^N), to the anisotropic setting.
  • 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 ...
  • 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 ...
  • A Special Family of Binary Forms, Their Invariant Theory, and Related Computations 
    Dethier, Christophe (University of Oregon, 2020-12-08)
    In this manuscript we study the family of diagonalizable forms, a special family of integral binary forms. We begin with a summary of definitions and known results relevant to binary forms, diagonalizable forms, Thue ...
  • A Structure Theorem for RO(C2)-graded Cohomology 
    May, Clover (University of Oregon, 2018-09-06)
    Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology ...
  • A(infinity)-structures, generalized Koszul properties, and combinatorial topology 
    Conner, Andrew Brondos, 1981- (University of Oregon, 2011-06)
    Motivated by the Adams spectral sequence for computing stable homotopy groups, Priddy defined a class of algebras called Koszul algebras with nice homological properties. Many important algebras arising naturally in ...
  • The A-infinity Algebra of a Curve and the J-invariant 
    Fisette, Robert (University of Oregon, 2012)
    We choose a generator G of the derived category of coherent sheaves on a smooth curve X of genus g which corresponds to a choice of g distinguished points P1, . . . , Pg on X. We compute the Hochschild cohomology of the ...
  • Abelian Arrangements 
    Bibby, Christin (University of Oregon, 2015-08-18)
    An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. We are interested in the topology of the complement of an arrangement. If the arrangement ...
  • 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 ...
  • Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A 
    Loubert, Joseph (University of Oregon, 2015-08-18)
    This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras $R_\alpha$ of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger ...
  • Algebraic Weak Factorization Systems in Double Categories 
    Schultz, Patrick (University of Oregon, 2014-09-29)
    We present a generalized framework for the theory of algebraic weak factorization systems, building on work by Richard Garner and Emily Riehl. We define cyclic 2-fold double categories, and bimonads (or bialgebras) and ...
  • An Odd Analog of Plamenevskaya's Invariant of Transverse Knots 
    Montes de Oca, Gabriel (University of Oregon, 2020-12-08)
    Plamenevskaya defined an invariant of transverse links as a distinguished class in the even Khovanov homology of a link. We define an analog of Plamenevskaya’s invariant in the odd Khovanov homology of Ozsváth, Rasmussen, ...
  • 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)
  • Approximate Diagonalization of Homomorphisms 
    Ro, Min (University of Oregon, 2015-08-18)
    In this dissertation, we explore the approximate diagonalization of unital homomorphisms between C*-algebras. In particular, we prove that unital homomorphisms from commutative C*-algebras into simple separable unital ...
  • AT-algebras from zero-dimensional dynamical systems 
    Herstedt, Paul (University of Oregon, 2020-09-24)
    We outline a particular type of zero-dimensional system (which we call "fiberwise essentially minimal"), which, together with the condition of all points being aperiodic, guarantee that the associated crossed product ...
  • Blocks in Deligne's category Rep(St) 
    Comes, Jonathan, 1981- (University of Oregon, 2010-06)
    We give an exposition of Deligne's tensor category Rep(St) where t is not necessarily an integer. Thereafter, we give a complete description of the blocks in Rep(St) for arbitrary t. Finally, we use our result on blocks ...
  • 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 ...
  • Categorical Actions on Supercategory O 
    Davidson, Nicholas (University of Oregon, 2016-11-21)
    This dissertation uses techniques from the theory of categorical actions of Kac-Moody algebras to study the analog of the BGG category O for the queer Lie superalgebra. Chen recently reduced many questions about this ...
  • 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 ...
  • Chern Character for Global Matrix Factorizations 
    Platt, David (University of Oregon, 2013-10-03)
    We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\O_X)$. Our formula takes values in a Cech model for Hochschild homology. ...

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