# Browsing Mathematics Theses and Dissertations by Title

## Results

• (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, ...
• (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, 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, 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 ...
• (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, 2011-06)
Motivated by the Adams spectral sequence for computing stable homotopy groups, Priddy defined a class of algebras called Koszul algebras with nice homological properties. Many important algebras arising naturally in ...
• (University of Oregon, 2012)
We choose a generator G of the derived category of coherent sheaves on a smooth curve X of genus g which corresponds to a choice of g distinguished points P1, . . . , Pg on X. We compute the Hochschild cohomology of the ...
• (University of Oregon, 2015-08-18)
An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. We are interested in the topology of the complement of an arrangement. If the arrangement ...
• (University of Oregon, 2015-08-18)
This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras $R_\alpha$ of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger ...
• (University of Oregon, 2014-09-29)
We present a generalized framework for the theory of algebraic weak factorization systems, building on work by Richard Garner and Emily Riehl. We define cyclic 2-fold double categories, and bimonads (or bialgebras) and ...
• (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, ...
• (University of Oregon, 2015-08-18)
In this dissertation, we explore the approximate diagonalization of unital homomorphisms between C*-algebras. In particular, we prove that unital homomorphisms from commutative C*-algebras into simple separable unital ...
• (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 ...
• (University of Oregon, 2010-06)
We give an exposition of Deligne's tensor category Rep(St) where t is not necessarily an integer. Thereafter, we give a complete description of the blocks in Rep(St) for arbitrary t. Finally, we use our result on blocks ...
• (University of Oregon, 2016-11-21)
This dissertation uses techniques from the theory of categorical actions of Kac-Moody algebras to study the analog of the BGG category O for the queer Lie superalgebra. Chen recently reduced many questions about this ...
• (University of Oregon, 2013-10-03)
We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\O_X)$. Our formula takes values in a Cech model for Hochschild homology. ...
• (2000)
The Orlik-Solomon algebra of a hyperplane arrangement first appeared from the Brieskorn and Orlik-Solomon theorems as the cohomology of the complement of this arrangement (if the ground field is complex). Later, it was ...
• (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 ...
• (University of Oregon, 2015-08-18)
This dissertation is concerned with representations of locally compact groups on different classes of Banach spaces. The first part of this work considers representations of compact groups by automorphisms of C*-algebras, ...
• (University of Oregon, 2017-09-06)
Working at the prime p = 3, we construct a stably finite spectrum, Z, with a v_2^1 self map f. Further, both Ext_A(H*(Z),Z_3) and Ext_A(H*(Z),H*(Z)) have a vanishing line of slope 1/16 in (t-s,s) coordinates, and the map ...