Browsing Mathematics Theses and Dissertations by Title
Now showing items 726 of 64

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 ... 
Frames Generated by Actions of Locally Compact Groups
(University of Oregon, 20161027)Let $G$ be a second countable, locally compact group which is either compact or abelian, and let $\rho$ be a unitary representation of $G$ on a separable Hilbert space $\mathcal{H}_\rho$. We examine frames of the form $\{ ... 
Generalized NearGroup Categories
(University of Oregon, 2012)We give an exposition of neargroup categories and generalized neargroup categories. We show that both have a pseudounitary structure. We complete the classification of braided neargroup categories and discuss the inherent ... 
Generalized selfintersection local time for a superprocess over a stochastic flow
(University of Oregon, 201006)This dissertation examines the existence of the selfintersection local time for a superprocess over a stochastic flow in dimensions d ≤ 3, which through constructive methods, gives a Tanaka like representation. The ... 
Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots
(University of Oregon, 2012)We produce explicit geometric representatives of nontrivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, CottaRamusino and Longoni to define cycles which live ... 
GKZ Hypergeometric Systems and Projective Modules in Hypertoric Category O
(University of Oregon, 20161027)In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fandKa ... 
Gluing Bridgeland's stability conditions and Z2equivariant sheaves on curves
(University of Oregon, 200906)We define and study a gluing procedure for Bridgeland stability conditions in the situation where a triangulated category has a semiorthogonal decomposition. As one application, we construct an open, contractible subset U ...