Now showing items 7-26 of 57

• #### Blocks in Deligne's category Rep(St) ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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, ...
• #### Crossed product C*-algebras by finite group actions with a generalized tracial Rokhlin property ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### Finite W-algebras of classical type ﻿

(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 ...
• #### Frames Generated by Actions of Locally Compact Groups ﻿

(University of Oregon, 2016-10-27)
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 Near-Group Categories ﻿

(University of Oregon, 2012)
We give an exposition of near-group categories and generalized near-group categories. We show that both have a pseudounitary structure. We complete the classification of braided near-group categories and discuss the inherent ...
• #### Generalized self-intersection local time for a superprocess over a stochastic flow ﻿

(University of Oregon, 2010-06)
This dissertation examines the existence of the self-intersection 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 non-trivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live ...
• #### GKZ Hypergeometric Systems and Projective Modules in Hypertoric Category O ﻿

(University of Oregon, 2016-10-27)
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'fand-Ka ...
• #### Gluing Bridgeland's stability conditions and Z2-equivariant sheaves on curves ﻿

(University of Oregon, 2009-06)
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 ...
• #### Graded representation theory of Hecke algebras ﻿

(University of Oregon, 2010-06)
We study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to ...
• #### Group Actions on Hyperplane Arrangements ﻿

(University of Oregon, 2012)
In this dissertation, we will look at two families of algebras with connections to hyperplane arrangements that admit actions of finite groups. One of the fundamental questions to ask is how these decompose into irreducible ...
• #### Group decompositions, Jordan algebras, and algorithms for p-groups ﻿

(University of Oregon, 2008-06)
Finite p -groups are studied using bilinear methods which lead to using nonassociative rings. There are three main results, two which apply only to p -groups and the third which applies to all groups. First, for finite ...