Browsing Mathematics Theses and Dissertations by Title
Now showing items 1837 of 64

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 ... 
Gluing manifolds with boundary and bordisms of positive scalar curvature metrics
(University of Oregon, 20170906)This thesis presents two main results on analytic and topological aspects of scalar curvature. The first is a gluing theorem for scalarflat manifolds with vanishing mean curvature on the boundary. Our methods involve tools ... 
Graded representation theory of Hecke algebras
(University of Oregon, 201006)We study the graded representation theory of the IwahoriHecke 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 pgroups
(University of Oregon, 200806)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 ... 
Homological Properties of Standard KLR Modules
(University of Oregon, 20170501)KhovanovLaudaRouquier algebras, or KLR algebras, are a family of algebras known to categorify the upper half of the quantized enveloping algebra of a given Lie algebra. In finite type, these algebras come with a family ... 
Infinite dimensional versions of the SchurHorn theorem
(University of Oregon, 201106)We characterize the diagonals of four classes of selfadjoint operators on infinite dimensional Hilbert spaces. These results are motivated by the classical SchurHorn theorem, which characterizes the diagonals of selfadjoint ... 
Koszul and generalized Koszul properties for noncommutative graded algebras
(University of Oregon, 200906)We investigate some homological properties of graded algebras. If A is an R algebra, then E (A) := Ext A ( R, R ) is an Ralgebra under the cup product and is called the Yoneda algebra. (In most cases, we assume R ... 
Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds
(University of Oregon, 20150818)Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)dimensional manifolds, with respect to forming the connected sum with (2n1)connected, (4n+1)dimensional manifolds that are ... 
Manifolds with indefinite metrics whose skewsymmetric curvature operator has constant eigenvalues
(University of Oregon, 2000)Relative to a nondegenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skewsymmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant ... 
Metrics of positive scalar curvature and generalised Morse functions
(University of Oregon, 200906)We study the topology of the space of metrics of positive scalar curvature on a compact manifold. The main tool we use for constructing such metrics is the surgery technique of Gromov and Lawson. We extend this technique ... 
Motives of Log Schemes
(University of Oregon, 20170906)This thesis introduces two notions of motive associated to a log scheme. We introduce a category of log motives à la Voevodsky, and prove that the embedding of Voevodsky motives is an equivalence, in particular proving ...