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    Studying quantum gravity via simplicial Lorentzian path integrals
    (University of Waterloo, 2026-06-01) Padua Arguelles, Jose de Jesus
    This thesis investigates the Lorentzian path integral as a framework for quantum gravity, focusing on how its off-shell causal structure shapes physical predictions. The work shows that different assumptions about causality strongly affect phenomena such as cosmological tunneling, black hole thermodynamics, and gravitational entropy. A central result is the discovery that certain off-shell causality violations in the Lorentzian path integral give rise to the Euclidean saddle points that dominate semiclassical calculations, providing a concrete mechanism through which Euclidean features emerge from fundamentally Lorentzian dynamics. To study these questions non-perturbatively, the thesis uses Regge calculus, a discrete version of General Relativity that makes Lorentzian path integrals computationally tractable. The framework enables detailed studies of two key settings: Euclidean de Sitter space and evaporating black holes. In the de Sitter case, Euclidean saddles are shown to govern both cosmological tunneling amplitudes and entropy-related state counting, requiring unusual off-shell geometries with singular causal structures. In the black hole context, the work develops a Regge-calculus approach to replica wormholes and reproduces the Page curve within a four-dimensional gravitational model that includes matter. Overall, the thesis advances both the conceptual understanding and computational treatment of Lorentzian quantum gravity, establishing Regge calculus as a powerful tool for studying quantum aspects of gravity.
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    Optimization-based Constrained Trajectory Generation for Autonomous Vehicles
    (University of Waterloo, 2026-06-01) Kolapalli, Venkata Kameswara Praneeth
    In this thesis, we study problems in constrained trajectory generation for autonomous vehicles with a focus on designing optimization-based algorithms. First, we investigate the problem of designing trajectories required to satisfy signal temporal logic specifications for non-holonomic car-like robots. Autonomous mobile robots are actively applied to execute complex tasks, such as package delivery, autonomous taxiing, and search-and-rescue. Signal Temporal Logic (STL) offers a powerful formalism for such complex tasks. We formulate the problem as a nonlinear program to generate trajectories for a multi-robot system with car-like robots to perform complex tasks specified with STL grammar. The proposed approach uses an exact closed-form nonlinear parameterization of the kinematics to evaluate the STL grammar in the NLP. We demonstrate the effectiveness and scalability of our algorithm in practice compared to a state-of-the-art baseline. Second, we also investigate the problem of designing trajectories with obstacle avoidance constraints for quadcopters. Often robots operate in obstacle-free spaces that can be approximated by orthogonal polytopes. We leverage this problem structure and design an algorithm that is massively scalable in practice. Initially, we study the combinatorial optimization problem of decomposing orthogonal polytopes into a minimum number of boxes. We design a novel integer linear program to solve the problem exactly and show that a simple rounding scheme recovers near-optimal solutions from the relaxed linear program in practice. Next, we heuristically select a subset of the boxes to traverse in and then study the continuous problem of generating piecewise trajectories constrained to stay within the selected subset of boxes. We formulate a biconvex optimization program by parametrizing the trajectory and design an algorithm to recover a locally optimal solution using convex alternating minimizations. Finally, we demonstrate that our algorithms are significantly faster than existing baselines and are scalable for large-scale real-world quadcopter scenarios. Our solution approaches focus on generating trajectories that are provably correct with optimization-based techniques. We demonstrate our algorithms on real world platforms to show that our formulation is tractable for robots in practice.
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    Towards Indistinguishable Photon Generation from Nanowire Quantum Dots
    (University of Waterloo, 2026-06-01) Gangopadhyay, Sayan
    Quantum photonic technologies require bright, deterministic sources of entangled photons. Applications such as quantum networks further demand high single-photon indistinguishability, a key requirement for quantum interference in protocols such as entanglement swapping. Semiconductor nanowire quantum dots are among the brightest on-demand sources of high-fidelity entangled photon pairs generated through the biexciton-exciton cascade. The highest values of indistinguishability from quantum dot sources are achieved using resonant excitation. However, implementing resonant excitation in nanowire quantum dots has remained a long-standing challenge due to the stringent laser suppression required in nanowire geometries. In this thesis, we establish a robust technique for resonant excitation of a quantum dot embedded in a tapered single-mode nanowire waveguide. By engineering mode matching between the incident laser and the nanowire-guided mode, efficient coupling to and from the quantum dot is achieved while simultaneously suppressing back-scattered laser light. This approach enables the realization of a one-dimensional atom, in which coherent single-photon reflection is observed. Furthermore, by combining mode matching with polarization-based rejection, we achieve laser suppression on the order of 10⁶, enabling the generation of single photons under pulsed resonant excitation. Under these conditions, we observe clear Rabi oscillations and strong antibunching in second-order correlation measurements. Two-photon interference measurements yield an indistinguishability of 0.41 at a temporal separation of 12.5 ns, indicating that residual decoherence mechanisms, such as charge noise, limit performance in the current devices. Motivated by this limitation, we propose a broadband nanowire cavity based on a quasi-bound state in the continuum (quasi-BIC) design. This cavity leverages interference between two resonances to simultaneously achieve a Purcell enhancement of 17, high extraction efficiency of 74%, and a directional emission with an 88% Gaussian overlap over a spectral bandwidth of 4 nm, sufficient to enhance both photons in the biexciton–exciton cascade. These results establish resonant excitation in nanowire quantum dots as a viable route toward generating indistinguishable single photons, while highlighting the role of residual decoherence mechanisms that currently limit performance. The proposed quasi-BIC cavity design further provides a pathway toward enhancing emission rates and photon indistinguishability in this platform. Furthermore, the realization of a one-dimensional atom in a nanowire platform opens new opportunities for exploring waveguide quantum electrodynamics, including emitter-mediated photon-photon interactions.
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    Enclosure to Enclosure: from Temagami Forest to the CMHC Post-War House
    (University of Waterloo, 2026-06-01) Zhou, Victoria
    Approximately two-thirds of Ontario, Canada is comprised of forests—making up more than one-fifth of all forests in Canada—and 90 percent of it is situated on public Crown Land. While forests are ecological lands, they are also geopolitically delineated territories and administrated provincially. Within Ontario’s system of administrated forests, Temagami Forest distinguishes itself as a site of settler-colonial experiments in property, territory, and forestry. Although the land is public, the woods are entangled with the practices of capitalist industry. Softwood dimensional lumber—colloquially referred to as wood studs or 2x4s—is the product of such capitalist interventions in the forest. The colonial impact of this material extends beyond the forest; it is essential to the development and construction of the single-family stick-frame house. This typology is implicitly associated with democracy, self-determination, and social mobility, remaining deeply tied to the institution of private property in the nation-state of Canada and the United States. Through review of literature, assembling an archive of present and historical maps, and site visits, I weave together a narrative which bridges different landscapes and scales of wood extraction. This thesis explores the use of surveying and mapping, forestry and logging administration systems, stick-frame construction methods, and the nationally distributed housing design catalogue as four mechanisms that link forested landscapes in Ontario to the dominant culture of single-family stick-frame house ownership. Throughout are also speculative pencil drawings that rethink the standard representational strategies for 2x4s and wood. I use the concept of assemblage to understand the cooperation between material and cultural aspects of dimensional lumber. Forests are not readily available “supplies” that fill the “demand” for domestic property; there are legal, cultural, material, and architectural mechanisms which transform woodlands into fungible wood prisms into stick-frame houses. The 2x4 as a narrative device to explore how the institution of property emerges across forests and stick-frame houses. Through the duality of the word “enclosure” I demonstrate how logics of capitalism enclose commons across different scales.
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    Investigation of Skin Epithelial Innate Immune Barrier Functions using a Xenopus laevis Cell Line
    (University of Waterloo, 2026-06-01) Chhabra, Prakriti
    Frog skin functions as both a physical and immunological barrier to the external environment. In addition to protection by antimicrobial peptides (AMPs) present at the skin surface, epithelial cells recognize pathogen-associated molecular patterns and coordinate local immune responses. While amphibian AMPs are well known for antimicrobial activity, their roles in regulating epithelial immunity and barrier function remain unclear, partly due to limited in vitro models. The objectives of this thesis were to use the Xenopus laevis epithelial-like cell line Xela DS2 to (1) explore whether two X. laevis AMPs, magainin II and PGLa, exert immunomodulatory effects on epithelial cells, and (2) develop an in vitro epithelial barrier model for studying anuran skin immunity. To support the first objective, Xela DS2 were examined for the presence of magainin II and PGLa transcripts and treated with AMPs or a synthetic analogue of viral double stranded RNA [poly(I:C)] to determine non-cytotoxic concentrations. Xela DS2 demonstrated little to no transcription of target AMPs. Magainin II or PGLa at concentrations ≥32 µM, or poly(I:C) at concentrations above 250 ng/mL, were cytotoxic to Xela DS2, and established non-cytotoxic concentrations for use in experiments. Initial attempts to study potential immunomodulatory activity of AMPs were unsuccessful due to an unanticipated cellular response to the vehicle control. In parallel, an air-liquid interface model was established, where cells formed highly restrictive barriers with TEER values >10,000 Ω·cm² prior to airlift and maintained above functional thresholds for 6-8 days post airlift. Barrier formation depended on seeding density and passage number, with lower-passage cells performing better. Collagen coating was not essential, and use of a mammalian ALI supplement appeared detrimental. Barrier integrity was supported by organized ZO-1 localization and reduced paracellular permeability. Together, these findings establish Xela DS2 as a platform to study epithelial barrier function, AMP activity, and host-pathogen interactions in frog skin.