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Mathematics Theses and Dissertations: Recent submissions
Now showing items 21-40 of 125
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(University of Oregon, 2022-10-04)We define a useful diagram for studying fixed-point-free involution words. Following the example of Little, we define a specific and a general bumping algorithm on these diagrams. These algorithms serve as the basis for ...
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(University of Oregon, 2022-10-04)We study stable homotopy through unstable methods applied to its representing infinite loop space, as pioneered by Curtis and Wellington. Using cohomology instead of homology, we find a width filtration whose subquotients ...
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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, 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, 2022-10-04)We study the diagrammatic representation theory of the group $Sp_4$ and the quantum group $U_q(\mathfrak{sp}_4)$, expanding on the previous results of Kuperberg about type $B_2= C_2$ webs. In particular, we construct a ...
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(University of Oregon, 2022-10-04)Let $p$ be an odd prime, and let $C_p$ denote the cyclic group of order $p$. We use equivariant surgery methods to classify all closed, connected $2$-manifolds with an action of $C_p$. We then use this classification in ...
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(University of Oregon, 2022-10-04)We use techniques in the shuffle and exterior algebras to present the partition functions for several log-gas models in terms of either the Hyperpfaffian or the Berezin integral of an appropriate alternating tensor. Our ...
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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, 2021-11-23)We resolve an open conjecture from algebraic geometry, which states that two generating functions for plane partition-like objects (the "box-counting" formulae for the Calabi-Yau topological vertices in Donaldson-Thomas ...
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(University of Oregon, 2021-09-13)This thesis is based on the article [16], which studies the integral? ? ?a? ?b? s ρ(x1,...,xN) max|xi −xj| min|xi −xj| |xi −xj| ij dx1 ...dxN KN i<j i<j i<j where K is an arbitrary p-field, ρ is a well-behaved function ...
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(University of Oregon, 2021-09-13)In this paper, we extend Manin and Schechtman's higher Bruhat orders for the symmetric group to higher Bruhat orders for non-longest words w in the symmetric group. We prove that the higher Bruhat orders of non-longest ...
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(University of Oregon, 2020-12-08)Plamenevskaya defined an invariant of transverse links as a distinguished class in the even Khovanov homology of a link. We define an analog of Plamenevskaya’s invariant in the odd Khovanov homology of Ozsváth, Rasmussen, ...
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(University of Oregon, 2020-12-08)In this manuscript we study the family of diagonalizable forms, a special family of integral binary forms. We begin with a summary of definitions and known results relevant to binary forms, diagonalizable forms, Thue ...
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(University of Oregon, 2020-09-24)We outline a particular type of zero-dimensional system (which we call "fiberwise essentially minimal"), which, together with the condition of all points being aperiodic, guarantee that the associated crossed product ...
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(University of Oregon, 2020-09-24)We give an explicit description of the category of Yoneda extensions of standard modules over KLR algebras for two special cases in Lie type A. In these two special cases, the A-infinity category structure of the Yoneda ...
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(University of Oregon, 2020-09-24)We prove that the partition function for tripartite double-dimer configurations of a planar bipartite graph satisfies a recurrence related to the Desnanot-Jacobi identity from linear algebra. A similar identity for the ...
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(University of Oregon, 2020-09-24)We study a certain sequence of moduli spaces of stable sheaves on a K3 surface of Picard rank 1 over $\mathbb{C}$. We prove that this sequence can be given the structure of a geometric categorical $\mathfrak{sl}_2$ action, ...
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(University of Oregon, 2020-09-24)Let C2 denote the cyclic group of order two. Given a manifold with a C2-action, we can consider its equivariant Bredon RO(C2)-graded cohomology. We first use a classification due to Dugger to compute the Bredon cohomology ...
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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, 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 ...
Now showing items 21-40 of 125