Browsing Mathematics Theses and Dissertations by Title
Now showing items 120 of 64

A(infinity)structures, generalized Koszul properties, and combinatorial topology
(University of Oregon, 201106)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 Ainfinity Algebra of a Curve and the Jinvariant
(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
(University of Oregon, 20150818)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
(University of Oregon, 20150818)This thesis consists of two parts. In the first we prove that the KhovanovLaudaRouquier 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
(University of Oregon, 20140929)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 2fold double categories, and bimonads (or bialgebras) and ... 
Approximate Diagonalization of Homomorphisms
(University of Oregon, 20150818)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)
(University of Oregon, 201006)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
(University of Oregon, 20161121)This dissertation uses techniques from the theory of categorical actions of KacMoody 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
(University of Oregon, 20131003)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 OrlikSolomon algebras
(2000)The OrlikSolomon algebra of a hyperplane arrangement first appeared from the Brieskorn and OrlikSolomon 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, NonClassifiability and Crossed Products and Rigidity Results for Lpoperator Algebras
(University of Oregon, 20150818)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
(University of Oregon, 20170906)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 (ts,s) coordinates, and the map ... 
Crossed product C*algebras by finite group actions with a generalized tracial Rokhlin property
(University of Oregon, 200806)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 nonsimple C*algebras and the tracial quasiRokhlin property
(University of Oregon, 201006)This dissertation consists of four principal parts. In the first, we introduce the tracial quasiRokhlin 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
(University of Oregon, 201006)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
(University of Oregon, 201006)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 Nonkequal Configuration Spaces of Graphs
(University of Oregon, 20161121)We prove that the nonkequal 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
(University of Oregon, 20170906)We construct a semiorthogonal 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
(University of Oregon, 20170906)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 Walgebras of classical type
(University of Oregon, 200906)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 ...