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Browsing Mathematics Theses and Dissertations by Title
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Now showing items 54-73 of 125
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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 ...
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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 ...
Now showing items 54-73 of 125