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Master of Arts / Department of Communications Studies / Timothy Steffensmeier / Due to a rising interest for degrees in higher education, more students with disabilities have enrolled in the university system. Still, accessibility issues on campuses suggest institutions are not meeting the needs of students in the classroom or through curricula. This study examines current academic adjustments and the lived experiences of students with disabilities in order to understand the ableist Othering phenomenon in higher education. Qualitative research methods have been commonly used to investigate the “disabled voice”; however, triangulation of such methodologies has been criticized for reinforcing Otherness. This study used a phenomenological design implementing rhetorical agency for disabled students to answer open-ended questions in semi-structured interviews about their lived experiences. Consequently, such interviews created a platform for social change. The author also reflects on his own lived experiences as a deaf student in higher education. Findings include major themes such as a percolation of institutional hegemony, a re-appropriation of stigma through “voice,” and a call for inclusive strategies. Results indicate disabled students experience discrimination likely due to organizational tension in their university institution. Further, this study elaborates on proposed policy changes to college classrooms on large university campuses. Contributions of this study lie in implications for the future of qualitative inquiry, including how current research practices could undergo methodological reinvention to examine the ableist Othering phenomenon.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Todd Easton / Graph theory is a widely researched topic. A graph contains a set of nodes and a set of edges. The nodes often represent resources such as machines, employees, or plant locations. Each edge represents the relationship between a pair of nodes such as time, distance, or cost. Integer programs are frequently used to solve graphical problems. Unfortunately, IPs are NP-hard unless P = NP, which implies that it requires exponential effort to solve them. Much research has been focused on reducing the amount of time required to solve IPs through the use of valid inequalities or cutting planes. The theoretically strongest cutting planes are facet defining cutting planes. This research focuses on the node packing problem or independent set problem, which is a combinatorial optimization problem. The node packing problem involves coloring the maximum number of nodes such that no two nodes are adjacent. Node packings have been applied to airline traffic and radio frequencies. This thesis introduces a new class of graphical structures called suns. Suns produce previously undiscovered valid inequalities for the node packing polyhedron. Conditions are provided for when these valid inequalities are proven to be facet defining. Sun valid inequalities have the potential to more quickly solve node packing problems and could even be extended to general integer programs through conflict graphs.

x, 81 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / 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 to decompose tensor products and classify tensor ideals in Rep(St). / Committee in charge: Victor Ostrik, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Jonathan Brundan, Member, Mathematics; Alexander Kleshchev, Member, Mathematics; Michael Kellman, Outside Member, Chemistry

In this work, we prove three types of results with the strategy that, together, the author believes these should imply the local version of Hilbert's Fifth problem. In a separate development, we construct a nontrivial topology for rings of map germs on Euclidean spaces. First, we develop a framework for the theory of (local) nonstandard Lie groups and within that framework prove a nonstandard result that implies that a family of local Lie groups that converge in a pointwise sense must then differentiability converge, up to coordinate change, to an analytic local Lie group, see corollary 6.3.1. The second result essentially says that a pair of mappings that almost satisfy the properties defining a local Lie group must have a local Lie group nearby, see proposition 7.2.1. Pairing the above two results, we get the principal standard consequence of the above work which can be roughly described as follows. If we have pointwise equicontinuous family of mapping pairs (potential local Euclidean topological group structures), pointwise approximating a (possibly differentiably unbounded) family of differentiable (sufficiently approximate) almost groups, then the original family has, after appropriate coordinate change, a local Lie group as a limit point. (See corollary 7.2.1 for the exact statement.) The third set of results give nonstandard renditions of equicontinuity criteria for families of differentiable functions, see theorem 9.1.1. These results are critical in the proofs of the principal results of this paper as well as the standard interpretations of the main results here. Following this material, we have a long chapter constructing a Hausdorff topology on the ring of real valued map germs on Euclidean space. This topology has good properties with respect to convergence and composition. See the detailed introduction to this chapter for the motivation and description of this topology.

<p>In this thesis, we explore techniques in statistics and persistent homology, which detect features among data sets such as graphs, triangulations and point cloud. We accompany our theorems with algorithms and experiments, to demonstrate their effectiveness in practice.</p><p></p><p>We start with the derivation of graph scan statistics, a measure useful to assess the statistical significance of a subgraph in terms of edge density. We cluster graphs into densely-connected subgraphs based on this measure. We give algorithms for finding such clusterings and experiment on real-world data.</p><p></p><p>We next study statistics on persistence, for piecewise-linear functions defined on the triangulations of topological spaces. We derive persistence pairing probabilities among vertices in the triangulation. We also provide upper bounds for total persistence in expectation. </p><p></p><p>We continue by examining the elevation function defined on the triangulation of a surface. Its local maxima obtained by persistence pairing are useful in describing features of the triangulations of protein surfaces. We describe an algorithm to compute these local maxima, with a run-time ten-thousand times faster in practice than previous method. We connect such improvement with the total Gaussian curvature of the surfaces.</p><p></p><p>Finally, we study a stratification learning problem: given a point cloud sampled from a stratified space, which points belong to the same strata, at a given scale level? We assess the local structure of a point in relation to its neighbors using kernel and cokernel persistent homology. We prove the effectiveness of such assessment through several inference theorems, under the assumption of dense sample. The topological inference theorem relates the sample density with the homological feature size. The probabilistic inference theorem provides sample estimates to assess the local structure with confidence. We describe an algorithm that computes the kernel and cokernel persistence diagrams and prove its correctness. We further experiment on simple synthetic data.</p> / Dissertation

We attack the question of BPS occupancy in a wide class of 4d N = 2 quantum field theories. We first review the Seiberg-Witten approach to finding the low energy Wilsonian effective action actions of such theories. In particular, we analyze the case of Gaiotto theories, which provide a large number of non-trivial examples in a unified framework. We then turn to understanding the massive BPS spectrum of such theories, and in particular their relation to BPS quivers. We present a purely 4d characterization of BPS quivers, and explain how a quiver's representation theory encodes the solution to the BPS occupancy problem. Next, we derive a so called mutation method, based on exploiting quiver dualities, to solve the quiver's representation theory. This method makes previously intractable calculations nearly trivial in many examples. As a particular highlight, we apply our methods to understand strongly coupled chambers in ADE SYM gauge theories with matter. Following this, we turn to the general story of quivers for theories of the Gaiotto class. We present a geometric approach to attaining quivers for the rank 2 theories, leading to a very elegant solution which includes a specification of quiver superpotentials. Finally, we solve these theories by an unrelated method based on gauging flavor symmetries in their various dual weakly coupled Lagrangian descriptions. After seeing that this method agrees in the rank 2 case, we will apply our new approach to the case of rank n. / Physics

<p>In this dissertation we study combinatorial Hodge Laplacians on simplicial com-</p><p>plexes using tools generalized from spectral graph theory. Specifically, we consider</p><p>generalizations of graph Cheeger numbers and graph random walks. The results in</p><p>this dissertation can be thought of as the beginnings of a new spectral theory for</p><p>simplicial complexes and a new theory of high-dimensional expansion.</p><p>We first consider new high-dimensional isoperimetric constants. A new Cheeger-</p><p>type inequality is proved, under certain conditions, between an isoperimetric constant</p><p>and the smallest eigenvalue of the Laplacian in codimension 0. The proof is similar</p><p>to the proof of the Cheeger inequality for graphs. Furthermore, a negative result is</p><p>proved, using the new Cheeger-type inequality and special examples, showing that</p><p>certain Cheeger-type inequalities cannot hold in codimension 1.</p><p>Second, we consider new random walks with killing on the set of oriented sim-</p><p>plexes of a certain dimension. We show that there is a systematic way of relating</p><p>these walks to combinatorial Laplacians such that a certain notion of mixing time</p><p>is bounded by a spectral gap and such that distributions that are stationary in a</p><p>certain sense relate to the harmonics of the Laplacian. In addition, we consider the</p><p>possibility of using these new random walks for semi-supervised learning. An algo-</p><p>rithm is devised which generalizes a classic label-propagation algorithm on graphs to</p><p>simplicial complexes. This new algorithm applies to a new semi-supervised learning</p><p>problem, one in which the underlying structure to be learned is flow-like.</p> / Dissertation

viii, 50 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the Markov trace which descends to STLd. Combining this point of view with Ocneanu's formula for the Markov trace and Young's seminormal form, we deduce a new state-sum formula for the Alexander polynomial. We also give a direct combinatorial proof of this result. / Committee in charge: Arkady Vaintrob, Co-Chairperson, Mathematics Jonathan Brundan, Co-Chairperson, Mathematics; Victor Ostrik, Member, Mathematics; Dev Sinha, Member, Mathematics; Paul van Donkelaar, Outside Member, Human Physiology