Browsing Mathematics Theses and Dissertations by Title
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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 ... 
Motivic Integral of K3 Surfaces over a NonArchimedean Field
(University of Oregon, 20140929)We prove a formula expressing the motivic integral of a K3 surface over C((t)) with semistable reduction in terms of the associated limit mixed Hodge structure. Secondly, for every smooth variety over a complete discrete ... 
Multinets in P^2 and P^3
(University of Oregon, 20131003)In this dissertation, a method for producing multinets from a net in P^3 is presented. Multinets play an important role in the study of resonance varieties of the complement of a complex hyperplane arrangement and very few ... 
Multiplier Theorems on Anisotropic Hardy Spaces
(University of Oregon, 2012)We extend the theory of singular integral operators and multiplier theorems to the setting of anisotropic Hardy spaces. We first develop the theory of singular integral operators of convolution type in the anisotropic ... 
Nonexistence of a stable homotopy category for pcomplete abelian groups
(University of Oregon, 200906)We investigate the existence of a stable homotopy category (SHC) associated to the category of p complete abelian groups [Special characters omitted]. First we examine [Special characters omitted] and prove [Special ... 
On Algebras Associated to Finite Ranked Posets and Combinatorial Topology: The Koszul, Numerically Koszul and CohenMacaulay Properties
(University of Oregon, 20140929)This dissertation studies new connections between combinatorial topology and homological algebra. To a finite ranked poset Γ we associate a finitedimensional quadratic graded algebra RΓ. Assuming Γ satisfies a combinatorial ...