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    Excluded Structures for Pinch-graphic Matroids and Tournaments
    (University of Waterloo, 2026-04-24) Xing, Yun
    In this thesis, we study several problems related to excluded structures in matroids and tournaments. For matroids, we focus on finding the excluded minors for pinch-graphic matroids. For tournaments, we bound the size of excluded induced subgraphs of k-degenerate tournaments and we bound the number of backedge graphs of a tournament that are P3-free or Kt-free. Furthermore, we introduce a new way to color the arcs of a tournament and we propose a conjecture that connects this coloring to tournaments that do not contain Paley tournaments as an induced subgraph. For pinch-graphic matroids, we prove that if M is minimally non-pinch-graphic and M is not 3-connected, then |M| ≤ 20. Furthermore, we characterize all minimally non-pinch-graphic matroids that are not 3-connected. For the 3-connected case, we prove that in a special case, a 3-connected but not internally 4-connected minimally non-pinch-graphic matroid has at most 21 elements. We also improve a characterization of 3-separations in pinch-graphic matroids by Guenin and Heo. For tournaments, we show that an excluded induced subgraph for 1-in(out)-degenerate tournaments has at most (k² + 5k + 6) / 2 vertices, and an excluded induced subgraph for 1-degenerate tournaments has at most k² + 5k + 6 vertices. We also prove that a tournament with n vertices can have at most exponentially many P3-free or Kt-free backedge graphs, despite there being n! backedge graphs for a tournament with n vertices. We then introduce a new way to arc-color a tournament T with the corresponding chromatic number denoted as χ_Δ(T). The rule is to arc-color a tournament such that every directed cycle of length 3 gets 3 distinct colors. We prove that for tournaments T with n vertices, the growth rate of χ_Δ(T) is Θ(log n).
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    Better Barns: A Toolkit to Retrofit
    (University of Waterloo, 2026-04-24) Walsh, Isaac
    Dairy barn architecture in Southern Ontario is a prominent typology which serves as an infrastructural backbone to Canada’s food production system and the families who operate them. Although farm buildings are historically distinguished by their passive design and vernacular construction techniques, many current applications of barn design have appeared in the form of large independent structures which have significantly altered the way pre-existing and historic barns function in relation to traditional farmstead space planning and building utilization. Although this model satisfies operational demand, it fails to address the potential adaptation of existing farm buildings or infrastructure which often become abandoned or demolished to keep up with agricultural expansion or policy change. This thesis examines the historic shifts within the dairy industry throughout the 20th century that led to specialized industrial farming as a reaction to the changing socioeconomic factors which challenged a shrinking population of farm families to keep up with increased demand for production and efficiency. Through the analysis of case studies, the mapping of dairy farm processes, and research of contemporary best practices in barn design and animal welfare in Ontario, this thesis proposes to develop a new set of barn adaptation strategies in the form of a design tool kit which allow existing dairy farmers without access to large upfront capital to re-use existing structures to meet evolving operational demand without the need for displacing, abandoning, or interrupting any of its critical real-time operations. These intervention strategies will be articulated in the form of an accessible how-to style guidebook, with applied results presented in the form of three design proposals on a selected dairy farm site to illustrate how adaptive re-use strategies can be implemented to help family farms continue operating within three distinct business models. The goals of introducing better re-use strategies not only addresses the issue of embodied carbon and waste in current construction practices, but also incentivizes existing farming populations with access to aging buildings to continue operating into the future while keeping up with contemporary demands in environmental stewardship, animal welfare, and economic sustainability.
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    Complex Dynamics of Multiphase Gas in X-ray Cooling Cores
    (University of Waterloo, 2026-04-24) Gingras, Marie-Joelle
    This thesis investigates the dynamics of baryons in galaxy clusters, from hot X-ray atmospheres to stars, by connecting multi-wavelength observations across physical scales. I focus on the interplay between radiative cooling and radio-mechanical active galactic nuclei (AGN) feedback, which governs the dynamics of multiphase gas, and ultimately the evolution of cooling cores. First, I establish the large-scale thermodynamic conditions that govern cooling in cluster cores. Using the X-ray thermodynamic profiles of 85 groups and clusters, I quantify the differences between cool core and non-cool core systems, and study how they vary with radius. After accounting for mass-driven scatter, I demonstrate that cooling core signatures can be observed to a substantial fraction of R₂₅₀₀ (the radius within which the mean density is 2500 times that of the critical density), showing that these thermodynamic conditions are not simply constrained to the very central region where multiphase gas is observed, but are indeed well-established extended structures. This large-scale framework sets the stage for the detailed physical processes occurring on smaller scales. Next, I probe the complex dynamics of multiphase gas and stars in the central tens of kpc of four brightest cluster galaxies: Abell 1835, PKS 0745−191, Abell 262 and RX J0820.9+0752, using integral field spectroscopy obtained using the Keck Cosmic Web Imager. First, I map the distribution and kinematics of the warm ionized gas in these systems. In three of our four targets, the central galaxy and the nebular gas have a relative velocity of ∼150 km s⁻¹, revealing a dynamically active core environment where cooling and feedback proceed in a moving reference frame. In Abell 1835 and PKS 0745−191, I investigate how AGN feedback directly interacts with multiphase gas. Their nebular gas is composed of two kinematic components: an extended, quiescent phase and a churned-up component closer to the AGN that is disturbed by radio jets and cavities. Analysis of the churned-up phase reveals nebular gas outflows, leading to the first measurements of cavity velocities from nebular gas. The cavities' low speeds likely indicate mass-loading from uplifted gas, a process that can locally stimulate cooling. Finally, I connect these dynamics to stellar kinematics and star formation histories in three of the systems. This analysis further supports that AGN feedback can stimulate localized cooling and star formation. Abell 1835 and PKS 0745−191, both with strong AGN feedback, have extended recent star formation in their cores, while RX J0820.9+0752, with little AGN activity, lacks recent star formation. Most directly, in Abell 1835, I find tentative evidence that blueshifted young stars cooled out of a redshifted nebular outflow and are now infalling, supporting feedback-stimulated cooling and star formation. Together, this thesis links the larger-scale thermodynamic properties of the intracluster medium to the smaller-scale dynamics of multiphase gas and stars in cooling cores.
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    Beyond the Frontier: Militarization, Representation, and Everyday Life in Dahiyeh
    (University of Waterloo, 2026-04-24) Soudki, Sarah
    Dahiyeh is often framed as a militarized area beyond the reach of the Lebanese government, but this is a flattened perspective that presents Lebanon as a ‘failed state’. An infamous part of Beirut, it is home to working class Beirutis, internally displaced Lebanese, refugees, and migrant workers. Its streets are populated with checkpoints, roadblocks, informal neighbourhood watches, and political posters, comprising an infrastructure of spatial violence which both the Lebanese state and state-like forces use to claim and maintain their territorial sovereignties. This infrastructure is dynamic. It disappears, reappears, and moves through time and space, making visible the complex and hybrid nature of territory and sovereignty within Dahiyeh. This spatial violence is accompanied by top-down visual representations that reinforce the predominant narrative of Dahiyeh as militarized, effectively selling the necessity of external intervention. This thesis argues that the everyday lives of Dahiyeh’s inhabitants and visitors reveal a far more complex picture. They unfold within a dense web of hybrid sovereignties in which daily entanglements and negotiations with spatial violence are routine. These encounters constitute more than ‘just’ resilience; they become acts of resistance through which residents of Dahiyeh counter the militarization of their home. I offer counter-representation as a bottom-up approach that foregrounds lived experience and focuses on small-scale interactions with urban space. Through site observation, photography, and written reflections, I analyze how Dahiyeh’s hybrid sovereignties entangle with the spatial violence of daily life. I expose how militarized representation flattens Dahiyeh, then contrast this with a collection of counter-representations. In a context so commonly understood through distant observation, these counter-representations reveal the everyday encounters with sovereignty that are so often overlooked in discourse of Beirut and Dahiyeh as contested, hybrid, and militarized. By combining conventional top-down understandings and representations of Dahiyeh with the fine-grained, specific lived experiences of its residents, this thesis offers a more nuanced understanding of Dahiyeh’s complexity and ever-shifting nature.
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    The Unreasonable Aesthetic of Mathematics in the Sciences
    (University of Waterloo, 2026-04-23) Naik, Armand
    Eugene Wigner was a Nobel prize winning physicist, recognized for his work related to fundamental symmetry principles. In his 1960 speech-turned-publication, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” he claimed that some applications of math are miraculous. He was amazed that mathematical concepts appear unexpectedly in the natural science of physics, and when they do appear, they are often inspired by intuitions of beauty. Still, applied mathematics shows accurate measurements with unparalleled regularity and precision. In his discussion, Wigner defines mathematics and physics before delving into the role and success of mathematics in the natural sciences. Yet estranged from the rest of the text, the example he opens with discusses the social sciences. Though Wigner can be read as providing an account of why math is justified, at least within physics, the application of math within social sciences, like economics, is left for the reader to ponder. The following is an extension of Wigner’s curiosity applied to the social sciences, with particular attention to the role of beauty in applied mathematics. The central research question is the following: do the same aesthetic principles that define the miraculous application of mathematics in physics, apply in economics? After examining Wigner’s (1960) original paper, I draw upon the work of Areezo Islami (2016), Mark Wilson (2000), Nancy Cartwright (1999), Jennifer Jhun (2016), and Philip Mirowski (2012) to develop aesthetic categories that serve three purposes: (1) they provide clear vocabulary for explaining why certain theories and applied mathematics are found convincing, by identifying the aesthetic principles that underwrite belief in them; (2) they enable the retrospective abstraction of successful theories, allowing us to abstract and articulate the aesthetic criteria of successful theories and then attempt to reverse engineer their success using those same aesthetic principles; and (3) they establish a standpoint for evaluating new ideas, either by assessing their conformity to existing aesthetic standards or by identifying the emergence of new ones.