# Mathematics Theses and Dissertations

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This collection contains some of the theses and dissertations produced by students in the University of Oregon Mathematics Graduate Program. Paper copies of these and other dissertations and theses are available through the UO Libraries.

## Recent Submissions

• (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 ...
• (University of Oregon, 2019-09-18)
In this thesis, we give two equivalent definitions for a group $G$ acting on a strictly-unitary-lax-2-functor $D:\CC\rightarrow\mathscr{B}$ from the cube category to the Burnside category. We then show that the natural ...
• (University of Oregon, 2019-09-18)
We extend a well known result of Uchiyama, which gives a sufficient condition for a family of smooth homogeneous multipliers to characterize the Hardy space H^1(R^N), to the anisotropic setting.
• (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. ...
• (University of Oregon, 2019-09-18)
We explore the canonical Grothendieck topology and a new homotopical analog. First we discuss a specific description of the covers in the canonical topology, which we then use to get a corollary of Giraud's Theorem. Second ...
• (University of Oregon, 2019-09-18)
We use combinatorial identities in the shuffle and exterior algebra to present hyperpfaffian formulations of partition functions for ß-ensembles with arbitrary probability measure when ß is a square integer. This is an ...
• (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 ...
• (University of Oregon, 2019-09-18)
In this dissertation, we study two main topics: superfusion categories, and embeddings of symmetric fusion categories into modular fusion categories. Using a construction of Brundan and Ellis, we give a formula relating ...
• (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 ...
• (University of Oregon, 2019-09-18)
In this thesis, we prove regularity theory for nonlinear fourth order and second order elliptic equations. First, we show that for a certain class of fourth order equations in the double divergence form, where the nonlinearity ...
• (University of Oregon, 2019-09-18)
We investigate relationships between some knot invariants and symmetries of knots. In the first chapter, we recall the definitions of knots, the symmetries we will investigate, and some classical knot invariants including ...
• (1945-06)
In making use of the theory of linear regression to obtain an estimation of a dependent variate from the information contained in an independent variate, one frequently is faced with the problem of having the independent ...
• (University of Oregon, 2019-04-30)
We place a differential on $\dot\UC_{\mathfrak{sl}_3}^+$ and show that $\dot\UC_{\mathfrak{sl}_3}^+$ is Fc-filtered. This gives a categorification of the positive half of quantum $\sl_3$ at a prime root of unity.
• (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 ...
• (University of Oregon, 2018-09-06)
We prove a nonpolarized analogue of the asymptotic characterization of T<sup>2</sup>-symmetric Einstein flow solutions completed recently by LeFloch and Smulevici. We impose a far weaker condition, but obtain identical ...
• (University of Oregon, 2018-09-06)
The present dissertation consists of four interconnected projects. In the first, we introduce and study what we call factorizable module algebras. These are $U_q(\mathfrak{g})$-module algebras $A$ which factor, potentially ...
• (University of Oregon, 2018-09-06)
Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology ...
• (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 ...
• (University of Oregon, 2018-09-06)
We compute the RO(C2)-graded Bredon cohomology of certain families of real and complex C2-equivariant Grassmannians.
• (University of Oregon, 2018-09-06)
We give asymptotics near the boundary for the distribution of the first exit time of the isotropic alpha-stable Levy process on bounded Lipschitz sets in real euclidean space. These asymptotics bear some relation to the ...