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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

• #### Dancing in the Stars: Topology of Non-k-equal Configuration Spaces of Graphs ﻿

(University of Oregon, 2016-11-21)
We prove that the non-k-equal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit ...
• #### Categorical Actions on Supercategory O ﻿

(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 ...
• #### The Geometry of quasi-Sasaki Manifolds ﻿

(University of Oregon, 2016-10-27)
Let (M,g) be a quasi-Sasaki manifold with Reeb vector field xi. Our goal is to understand the structure of M when g is an Einstein metric. Assuming that the S^1 action induced by xi is locally free or assuming a certain ...
• #### GKZ Hypergeometric Systems and Projective Modules in Hypertoric Category O ﻿

(University of Oregon, 2016-10-27)
In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fand-Ka ...
• #### Frames Generated by Actions of Locally Compact Groups ﻿

(University of Oregon, 2016-10-27)
• #### Approximate Diagonalization of Homomorphisms ﻿

(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 ...
• #### Algebraic Weak Factorization Systems in Double Categories ﻿

(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 ...
• #### Motivic Integral of K3 Surfaces over a Non-Archimedean Field ﻿

(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 ...
• #### On Algebras Associated to Finite Ranked Posets and Combinatorial Topology: The Koszul, Numerically Koszul and Cohen-Macaulay Properties ﻿

(University of Oregon, 2014-09-29)
This dissertation studies new connections between combinatorial topology and homological algebra. To a finite ranked poset Γ we associate a finite-dimensional quadratic graded algebra RΓ. Assuming Γ satisfies a combinatorial ...
• #### The Tracial Rokhlin Property for Countable Discrete Amenable Group Actions on Nuclear Tracially Approximately Divisible C*-Algebras ﻿

(University of Oregon, 2014-09-29)
In this dissertation we explore the question of existence of a property of group actions on C*-algebras known as the tracial Rokhlin property. We prove existence of the property in a very general setting as well as specialise ...
• #### Topics in Random Walks ﻿

(University of Oregon, 2013-10-03)
We study a family of random walks defined on certain Euclidean lattices that are related to incidence matrices of balanced incomplete block designs. We estimate the return probability of these random walks and use it to ...