Now showing items 1-20 of 64

• #### A(infinity)-structures, generalized Koszul properties, and combinatorial topology ﻿

(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 ﻿

(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, 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 ﻿

(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 ﻿

(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 ﻿

(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) ﻿

(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, ...
• #### Constructing a v2 Self Map at p=3 ﻿

(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 ﻿

(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 ...
• #### Equivariant Derived Categories Associated to a Sum of Potentials ﻿

(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 ﻿

(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 ﻿

(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 ...