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  • Takahashi, Ryan (University of Oregon, 2020-09-24)
    We study a certain sequence of moduli spaces of stable sheaves on a K3 surface of Picard rank 1 over $\mathbb{C}$. We prove that this sequence can be given the structure of a geometric categorical $\mathfrak{sl}_2$ action, ...
  • Stephens, Andrew (University of Oregon, 2019-04-30)
    We place a differential on $\dot\UC_{\mathfrak{sl}_3}^+$ and show that $\dot\UC_{\mathfrak{sl}_3}^+$ is Fc-filtered. This gives a categorification of the positive half of quantum $\sl_3$ at a prime root of unity.
  • 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.
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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, ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...

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