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Browsing Mathematics Theses and Dissertations by Title
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Now showing items 49-68 of 125
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(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 ...
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(University of Oregon, 2017-09-06)This thesis presents two main results on analytic and topological aspects of scalar curvature. The first is a gluing theorem for scalar-flat manifolds with vanishing mean curvature on the boundary. Our methods involve tools ...
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(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 ...
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(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 ...
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(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 ...
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(University of Oregon, 2018-09-06)In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms ...
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(University of Oregon, 2022-10-26)Let $C_l$ denote the cyclic group of prime order $l$ and let $k$ be a field. We define a Mackey $\underline{k}$-algebra $\underline{k}[x_\theta]$ which is constructed by adjoining a free commutative variable to the free ...
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(University of Oregon, 2017-05-01)Khovanov-Lauda-Rouquier 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 ...
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(University of Oregon, 2011-06)We characterize the diagonals of four classes of self-adjoint operators on infinite dimensional Hilbert spaces. These results are motivated by the classical Schur-Horn theorem, which characterizes the diagonals of self-adjoint ...
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(University of Oregon, 2018-10-31)The Kazhdan-Lusztig polynomial of a matroid M, denoted P_M( t ), was recently defined by Elias, Proudfoot, and Wakefield. These polynomials are analogous to the classical Kazhdan-Lusztig polynomials associated with Coxeter ...
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(University of Oregon, 2009-06)We investigate some homological properties of graded algebras. If A is an R -algebra, then E (A) := Ext A ( R, R ) is an R-algebra under the cup product and is called the Yoneda algebra. (In most cases, we assume R ...
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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 ...
Now showing items 49-68 of 125