Now showing items 1-20 of 64

    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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. ...
    • Cohomology of the Orlik-Solomon algebras 

      Pearson, Kelly Jeanne, 1970- (2000)
      The Orlik-Solomon algebra of a hyperplane arrangement first appeared from the Brieskorn and Orlik-Solomon theorems as the cohomology of the complement of this arrangement (if the ground field is complex). Later, it was ...
    • Compact Group Actions on C*-algebras: Classification, Non-Classifiability and Crossed Products and Rigidity Results for Lp-operator Algebras 

      Gardella, Eusebio (University of Oregon, 2015-08-18)
      This dissertation is concerned with representations of locally compact groups on different classes of Banach spaces. The first part of this work considers representations of compact groups by automorphisms of C*-algebras, ...
    • Constructing a v2 Self Map at p=3 

      Reid, Benjamin (University of Oregon, 2017-09-06)
      Working at the prime p = 3, we construct a stably finite spectrum, Z, with a v_2^1 self map f. Further, both Ext_A(H*(Z),Z_3) and Ext_A(H*(Z),H*(Z)) have a vanishing line of slope 1/16 in (t-s,s) coordinates, and the map ...
    • Crossed product C*-algebras by finite group actions with a generalized tracial Rokhlin property 

      Archey, Dawn Elizabeth, 1979- (University of Oregon, 2008-06)
      This dissertation consists of two related parts. In the first portion we use the tracial Rokhlin property for actions of a finite group G on stably finite simple unital C *-algebras containing enough projections. The ...
    • Crossed product C*-algebras of certain non-simple C*-algebras and the tracial quasi-Rokhlin property 

      Buck, Julian Michael, 1982- (University of Oregon, 2010-06)
      This dissertation consists of four principal parts. In the first, we introduce the tracial quasi-Rokhlin property for an automorphism α of a C *-algebra A (which is not assumed to be simple or to contain any projections). ...
    • Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus 

      Sun, Wei, 1979- (University of Oregon, 2010-06)
      This dissertation is a study of the relationship between minimal dynamical systems on the product of the Cantor set ( X ) and torus ([Special characters omitted]) and their corresponding crossed product C *-algebras. For ...
    • The crossed product of C(X) by a free minimal action of R 

      Liang, Hutian (University of Oregon, 2010-06)
      In this dissertation, we will study the crossed product C*-algebras obtained from free and minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. We first define stable ...
    • Dancing in the Stars: Topology of Non-k-equal Configuration Spaces of Graphs 

      Chettih, Safia (University of Oregon, 2016-11-21)
      We prove that the non-k-equal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit ...
    • Equivariant Derived Categories Associated to a Sum of Potentials 

      Lim, Bronson (University of Oregon, 2017-09-06)
      We construct a semi-orthogonal decomposition for the equivariant derived category of a hypersurface associated to the sum of two potentials. More specifically, if $f,g$ are two homogeneous poynomials of degree $d$ defining ...
    • Faithful tropicalization of hypertoric varieties 

      Kutler, Max (University of Oregon, 2017-09-06)
      The hypertoric variety M_A defined by an arrangement A of affine hyperplanes admits a natural tropicalization, induced by its embedding in a Lawrence toric variety. In this thesis, we explicitly describe the polyhedral ...
    • Finite W-algebras of classical type 

      Brown, Jonathan, 1975- (University of Oregon, 2009-06)
      In this work we prove that the finite W -algebras associated to nilpotent elements in the symplectic or orthogonal Lie algebras whose Jordan blocks are all the same size are quotients of twisted Yangians. We use this to ...