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    On the effective algebraic geometry of determinantal varieties
    (University of Waterloo, 2026-10-22) Gopalakrishnan, Sriram
    The central objects of study in this thesis are varieties defined by rank deficiencies of matrices with polynomial entries, which are known as determinantal varieties. We consider effective questions about these varieties from two distinct perspectives. The first part of this thesis concerns computational results in the arithmetic complexity model, where basic field operations have unit cost. From classical results on free resolutions of determinantal ideals, we extract information about the syzygy modules of determinantal ideals, and use this information to adapt existing general-purpose Gröbner basis algorithms to determinantal ideals. This leads us to new algorithms to solve zero-dimensional determinantal polynomial systems and polynomial optimisation problems. We give complexity analyses of our algorithms, and in so doing, show that they improve upon the state-of-the-art. The central problem considered in the second part of this thesis is to bound heights of determinantal varieties. By way of new constructions in arithmetic integral geometry, we give exact values for Mahler measures of determinantal resultants. Coupled with a determinantal analogue of the standard u-resultant, this enables us to bound heights of Chow forms of determinantal varieties.
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    Dopant–Carrier Exchange Coupling in Mn2+-Doped Metal Halide Perovskite Nanocrystals
    (University of Waterloo, 2026-10-22) Yeh, I-Hsuan
    While early studies of lead halide perovskites (LHPs) have focused on their tunable optoelectronic properties and applications in photovoltaics and optoelectronics, their rich spin-related properties, including strong spin–orbit coupling (SOC), long spin relaxation and coherence times, as well as their strong coupling to the lattice, have more recently attracted attention for spin-based functionalities. These characteristics position LHPs as promising candidates for spintronic and quantum information applications. Incorporation of magnetic ions into the perovskite lattice introduces additional spin degree of freedom, giving rise to hybrid materials that combine semiconducting behavior with magnetic interactions. Such dopant-induced exchange interactions enable coupling between localized spins and band carriers, providing a pathway toward spin-dependent transport in future spintronic devices. However, compared to conventional II–VI chalcogenide semiconductors, magnetic-dopant-induced exchange interactions in halide perovskites remain less well understood. In this thesis, magnetic exchange interactions in Mn2+-doped metal halide perovskite nanocrystals (NCs) are investigated using magnetic circular dichroism (MCD) spectroscopy to probe dopant–exciton coupling. This thesis begins with three-dimensional (3D) CsPbCl3 NCs as a model host lattice for magneto-optical investigation, owing to their high Mn2+ miscibility via the hot-injection method and an efficient energy transfer. At cryogenic temperatures, the excitonic MCD responses are significantly enhanced relative to pristine NCs and exhibit magnetic-field-dependent saturation, consistent with magnetization arising from paramagnetic Mn2+ (d5) spins. Distinct from conventional II–VI chalcogenide diluted magnetic semiconductors (DMSs), the MCD spectra display absorption-like line shapes rather than inverted derivative features, suggesting differences in coupling to band-edge carriers in LHPs. The similar MCD line shapes observed for both the band-edge and higher-lying excitonic transitions further provide insight into the origin of the coupling of higher-energy states to Mn2+. The effect of heterohalide alloying on dopant–exciton interactions is further examined by incorporating Br- into the CsPbCl3 lattice. The resulting excitonic magneto-optical responses show a pronounced enhancement relative to the pure Cl system, which is associated with anomalous kinetic exchange involving Mn2+ d electrons and the s-orbital-derived valence band maximum (VBM). Temperature-dependent MCD measurements additionally provide an alternative approach to estimate the Zeeman splitting of band-edge states. These findings contribute to understanding of spin-induced excitonic Zeeman effects in lead halide perovskite DMSs with inverted electronic structures relative to conventional chalcogenide semiconductors. The investigation of Mn2+-induced magnetic coupling is further extended beyond 3D LHPs to zero-dimensional (0D) Mn2+-doped Cs4PbCl6 NCs. Despite sharing the same PbCl6 motif with 3D CsPbCl3, spin-induced MCD responses in this 0D lattice exhibit a contribution comparable to the intrinsic component, contrasting with the exchange-dominated behavior of the 3D counterpart. The resolved exchange component retains an absorption-like line shape associated with band-edge transitions, indicating selective coupling of Mn2+ spins to the electronic states of the isolated PbCl6 units. Finally, magneto-optical investigations of lead-free, bismuth-based halide double perovskites (HDPs) reveal the presence of magnetic exchange interactions. The relatively weak exchange interaction in HDPs reflects the role of chemical heterogeneity in shaping excitonic properties within the rock-salt lattice. The sign inversion observed in the MCD spectra upon Mn2+ doping suggests an exchange mechanism distinct from that in lead-based halide perovskites, underscoring the influence of band-edge electronic structure on magnetic coupling. Overall, the findings of this thesis demonstrate the tunability of spin-dependent interactions in halide perovskites through Mn2+ doping, establishing a framework for understanding dopant–exciton coupling across diverse perovskite lattices.
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    Disruptive climate policy from wells to wheels: Integrating demand- and supply-side climate governance in oil-producing states
    (University of Waterloo, 2026-10-22) Greene, Sarah
    Fossil fuel-producing states occupy a paradoxical position within climate governance. Many have adopted increasingly ambitious climate policies, including net-zero commitments, renewable energy deployment strategies, and transportation electrification programs. Yet many of these same jurisdictions continue to expand fossil fuel production and export infrastructure. As a result, climate ambition and fossil fuel dependence increasingly proceed in parallel. This tension raises a critical governance challenge: how can fossil fuel-producing states accomplish deep decarbonization while simultaneously reducing their economic, political, and institutional dependence on oil and gas? This dissertation examines that question through three interconnected manuscripts that explore the relationship between demand-side and supply-side climate governance in fossil fuel-producing states. Situated within global environmental governance and drawing on comparative political economy, carbon lock-in, and sustainability transitions scholarship, the dissertation applies an analytical framework centred on institutions, interests, and ideas to examine the political conditions that enable or constrain deeper transitions away from fossil fuels, particularly oil. The first article, published in International Environmental Agreements: Politics, Law and Economics in 2024, examines Denmark’s emergence as a global first-mover in supply-side climate governance through its decision to phase out future oil and gas extraction in the North Sea. The analysis addresses the political, institutional, and ideational conditions that enabled an explicit fossil fuel phase-out policy to emerge in a fossil fuel-producing economy. The findings show that supply-side climate governance is politically feasible and emphasize the role of national first movers in shaping emerging forms of global fossil fuel governance. The second article, accepted with revisions at Energy Research & Social Science in June 2026, explores the demand side of climate governance through a comparative examination of transportation electrification in Norway and Canada. The findings show that ambitious demand-side decarbonization can substantially reduce emissions, boost technological change, and build durable political support for climate action. However, transportation electrification does not automatically reduce fossil fuel production. Rather, the analysis shows that demand-side transitions can create important political, economic, and institutional conditions for broader transition while remaining compatible with continued extraction under existing political-economic arrangements. Building on these findings, the third article, accepted with revisions at The Extractive Industries and Society Journal in June 2026, examines Canada’s challenge of integrating demand-side and supply-side climate policy within a deeply carbon-intensive federal political economy. Drawing on insights from Denmark and Norway, the analysis demonstrates how institutions, interests, and ideas persist to reproduce fossil fuel dependence while identifying pathways for aligning both sides of the climate policy “scissors” within a broader decarbonization strategy. Collectively, the dissertation argues that deep decarbonization in fossil fuel-producing states requires more than reducing emissions or constraining fossil fuel production in isolation. It requires transforming the institutions, interests, and ideas that reproduce fossil fuel dependence and politically integrating demand-side and supply-side climate governance. In doing so, the dissertation contributes to scholarship on carbon lock-in and transition politics by shifting attention from explaining the persistence of fossil fuel dependence toward understanding the political conditions under which fossil fuel-producing states may begin to move beyond it. The findings further suggest that demand-side transitions may create political and economic conditions that increase the feasibility of future supply-side climate governance, pointing toward a potential sequencing dynamic in pathways toward deep decarbonization.
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    Craftsmanship's Value: Exploring the Shifting Role of the Maker in Contemporary Slip-Cast Fabrication
    (University of Waterloo, 2026-10-22) Haddy, Candace
    As technologies become increasingly integrated into production, the maker’s relationship with material is transferred from direct physical engagement to roles as programmer and operator, leading to a risk in loss of craftsmanship. While technological advancement has increased the efficiency and possibilities of architectural production by reducing time, labour, and cost, it has also altered the relationship between designers, makers, and materials. This raises questions about how values of craftsmanship such as reflective judgement learned through making and a responsibility toward the user and society, can persist within contemporary fabrication. This thesis investigates the role and value of craftsmanship in contemporary production processes by speaking with craftsmen through field research and working with slip casted ceramics, a pottery-forming process using absorbent molds with liquid clay (slip), to design and produce a screen system. Field research examines slip casting across different scales and methods of production through visits to Bryan Hopkins - an expert in small-scale slip casting, Ludowici Roof Tiles - a large-scale production facility for ceramic architectural components, Joshua Stein at Radical Craft - an experimental ceramicist who pushes the capabilities of fabrication methods, and a variety of toilet manufacturing facilities - high-quality mass production facilities of slip casted ceramic toilets. Each case study adapts the traditional slip casting process toward innovation or efficiency, revealing different values and motivations behind the maker’s choice of technique. These findings inform research through fabrication in which the identified methods and design goals are tested through the fabrication of a slip-cast screen system, providing a means for further analysis of craftsmanship and its role in contemporary craft. The cases studies and fabrication research are focused on the shift in knowledge, tools, and material connection from handcraft to contemporary machine fabrication, which can be further understood through architect and researcher Dr. Christoph Schindler’s framework of fabrication technology and evolution of techniques. Schindler describes fabrication processes as a continuous development with three waves of processing technology - hand tool, machine-tool, and information-tool technology, relating to evolving industrial developments and technological introductions. While this evolution can optimize production and expand its possibilities, the research examines the tensions and consequences that arise when knowledge shifts away from the craftsperson, particularly the potential loss of craftsmanship. As material and process knowledge enables informed design decisions, transferring this knowledge from the human to machines and digital information can distance the designer from the material and, consequently, from their responsibility toward the environments they create. This physical design analysis establishes the role and value of craftsmanship within contemporary production while informing a slip-cast fabrication methodology that incorporates these values. The research is evaluated through the conclusions drawn from comparing the values embedded within different approaches to production across varying scales and design intentions.
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    Children's Exploration Distinguishes Necessary and Merely Possible Outcomes
    (American Psychological Association, 2026) Andreuccioli, Luisa; Mazor, Sophie; Begus, Katarina; Bonawitz, Elizabeth; Dension, Stephanie; Walker, Caren M.
    Preschoolers often fail tasks that require that they select between a necessary and a merely possible outcome. Prior work has interpreted these failures as evidence that children hold a minimal representation of possibility or as reflecting performance factors. However, all previous paradigms have operationalized children’s modal understanding as a discrete choice or outcome, making it difficult to distinguish between these accounts. We introduce a continuous measure of search behavior to assess how modal status regulates exploration. American 3- and 4-year-olds (48% female, 52% male) searched for an object dropped into one of two boxes after passing through a set of either transparent (yielding a single necessary location) or opaque tubes (yielding two possible locations). In Experiment 1, both age groups spent relatively less time searching the first location they approached and switched more often when the outcomes were merely possible than when the outcome was necessary. Experiment 2 replicated this pattern in a touchscreen version. Experiment 3 demonstrated the same effect while controlling for object tracking by equating inferential demands across conditions. Across experiments, children’s search behavior was aligned with modal status, indicating that representations of necessity and possibility guide exploration before children reliably succeed on discrete choice modal reasoning tasks. These results suggest children’s early sensitivity to modal concepts is expressed in their continuous search behavior, shaping real-time decision making. Our findings inform theories of modal reasoning in early childhood, suggesting that modal representations may be more readily expressed through graded patterns of exploration rather than discrete choices.