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Browsing Mathematics Theses and Dissertations by Title
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Now showing items 60-79 of 125
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(University of Oregon, 2022-10-04)Diophantine analysis is an area of number theory concerned with finding integral solutions to polynomial equations defined over the rationals, or more generally over a number field. In some cases, it is possible to associate ...
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(University of Oregon, 2024-01-09)This thesis describes the Fano scheme $F(Y)$ of lines on a general cubic threefold $Y$ containing a plane over a field $k$ of characteristic different from $2$. One irreducible component of $F(Y)$ is birational (over $k$) ...
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(University of Oregon, 2015-08-18)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 (2n-1)-connected, (4n+1)-dimensional manifolds ...
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(University of Oregon, 2019-09-18)Mackey functors over the group Z/2 are useful in the study of Z/2-equivariant cohomology. In this dissertation we establish results which are useful for homological algebra computations for certain Mackey rings over Z/2. ...
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Manifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvalues (University of Oregon, 2000)Relative to a non-degenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skew-symmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant ...
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(University of Oregon, 2024-01-09)In the unstable range, topological vector bundles over finite CW complexes are difficult to classify in general. Over complex projective spaces \mathbb{C}P^n, such bundles are far from being fully classified, or even ...
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(University of Oregon, 2019-09-18)The classification of simply connected manifolds admitting metrics of positive scalar curvature of initiated by Gromov-Lawson, at its core, relies on a careful geometric construction that preserves positive scalar curvature ...
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(University of Oregon, 2009-06)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 ...
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(University of Oregon, 2022-10-04)In this dissertation we examine generalized Schur algebras, as defined by Kleshchev and Muth. Given a quasi-hereditary superalgebra $A$, Kleshchev and Muth proved that for $n \geq d$, the generalized Schur algebra $T^A ...
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(University of Oregon, 2022-10-04)In this thesis, we study $A_\infty$-structures arising from derived categories of certain algebraic curves. More precisely, we consider pairs $(\mathcal{O}_C,\mathcal{O}_D)$, where $C$ is an irreducible projective curve ...
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(University of Oregon, 2020-09-24)We study the moduli space M of twisted Hermite-Einstein connections on a vector bundle over a K3 surface X. We show that the universal bundle can be viewed as a family of stable vector bundles over M parameterized by X, ...
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(University of Oregon, 2019-09-18)We consider two K3 surfaces defined over an arbitrary field, together with a smooth proper moduli space of stable sheaves on each. When the moduli spaces have the same dimension, we prove that if the etale cohomology groups ...
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(University of Oregon, 2017-09-06)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 ...
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(University of Oregon, 2014-09-29)We prove a formula expressing the motivic integral of a K3 surface over C((t)) with semi-stable reduction in terms of the associated limit mixed Hodge structure. Secondly, for every smooth variety over a complete discrete ...
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(University of Oregon, 2013-10-03)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 ...
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(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 ...
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(University of Oregon, 2020-02-27)Let Man* denote the category of closed, connected, oriented and based 3- manifolds, with basepoint preserving dieomorphisms between them. We show that the Heegaard Floer invariants yield functors from Man* to the category ...
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(University of Oregon, 2018-04-10)We begin by reviewing the theory of NC-schemes and NC-smoothness, as introduced by Kapranov in \cite{Kapranov} and developed further by Polishchuk and Tu in \cite{PT}. For a smooth algebraic variety $X$ with a ...
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(University of Oregon, 2024-01-09)In this paper, we build on the work of Lipshitz, Ozsv\'{a}th, and Thurston by constructing an algorithm that generates a weighted $A_\infty$-diagonal given a family of contractions of the weighted associahedron complexes. ...
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(University of Oregon, 2009-06)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 ...
Now showing items 60-79 of 125