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.
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 ...
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 ...
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 ...
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, ...
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 ...
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, ...
Gartner, Michael(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 ...
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 ...
Hiserote, Martin(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.
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. ...
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 ...
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 ...
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 ...
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 ...
Burdick, Bradley(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 ...
Bhattacharya, Arunima(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 ...
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 ...
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 ...
Stephens, Andrew(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.
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 ...