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    Crystal Structures and Nonlinear Optical Properties of Semiconducting Main Group Chalcogenides
    (University of Waterloo, 2026-09-25) Licskai, Tristan
    I have investigated ten compounds where the experimental crystal structures have not been reported. Of these compounds, five are noncentrosymmetric, two are oxychalcogenides, and four are new structure types. The noncentrosymmetric compounds discovered are part of two distinct families: A2BQ4 and A6M4T4Q16 (A = Sr–Ba; M = Cu–Ag; B = Si–Sn; Q = O–Te). The A2BQ4 family contains Sr2SiSe4 (P21, a = 6.8866(19) Å, b = 7.0062(19) Å, c = 8.520(2) Å, β = 108.200(6)°) and Sr2SnSe4 (Ama2, a = 10.4802(10) Å, b = 10.6965(10) Å, c = 7.5411(7) Å). DFT calculations revealed Sr2SiSe4 and Sr2SnSe4 to have direct band gaps of 2.31 eV and 2.05 eV, respectively. Sr2SiSe4 was determined to have a second harmonic generation intensity of 0.5 × AGS, a laser-induced damage threshold of 3.1 × AGS, and a thermal conductivity of 0.46 W m-1 K-1 at 523 K. The A6M4T4Q16 family contains Sr6Ag3.91Si4Se16 (I4¯3d, a = 14.621(2) Å), Sr6Ag3.63Sn4Se16 (I4¯3d, a = 14.9295(5) Å), and Sr6Cu2.33Ag1.55Si4Se16 (I4¯3d, a = 14.4904(5) Å). DFT calculations revealed Sr6Ag3.91Si4Se16, Sr6Ag3.63Sn4Se16, and Sr6Cu2.33Ag1.55Si4Se16 to have direct band gaps of 1.14 eV, 1.09 eV, and 1.28 eV, respectively. Sr6Ag3.63Sn4Se16 was determined to have a second harmonic generation intensity of 0.5 × AGS, and a laser-induced damage threshold of 3.3 × AGS. The centrosymmetric compounds discovered are part of three distinct families: ABQ3, A3B2Q7, and oxychalcogenides. The ABQ3 family contains SrSiSe3 (P21/c, a = 6.6948(2) Å, b = 17.4606(4) Å, c = 15.8647(3) Å, β = 117.0100(10)°) and BaGeSe3 (P21/c, a = 15.6603(7) Å, b = 6.0379(3) Å, c = 14.0072(6) Å, β = 116.3830(10)°). DFT calculations revealed SrSiSe3 and BaGeSe3 to have band gaps of 2.15 eV and 1.65 eV, respectively. The A3B2Q7 family contains Sr3Sn2S7 (C2/m (no. 12), a = 23.207(2) Å, b = 7.9768(8) Å, c = 17.216(3) Å, β = 132.1738(17)°), which possesses rare SnS5 polyhedra in addition to SnS4 tetrahedra. DFT calculations revealed Sr3Sn2S7 to have a direct band gap of 1.10 eV. The oxychalcogenide family contains Sr3Ge3OS8 (Pnma, a = 15.6628(6) Å, b = 13.9919(5) Å, c = 6.6687(3) Å) and Ba4Ge2O3Se5 (Pnma, a = 11.536(14) Å, b = 10.539(11) Å, c = 11.836(13) Å). DFT calculations revealed Sr3Ge3OS8 and Ba4Ge2O3Se5 to have band gaps of 2.55 eV and 2.25 eV, respectively.
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    Quantum Information Probes in Holography: Shell Geometries and Black Hole Singularities
    (University of Waterloo, 2026-09-25) Joerstad, Eivind Hilmen
    A remarkable aspect of the AdS/CFT correspondence and related holographic dualities is the way quantities related to quantum information in the non-gravitational boundary theory are geometrized by the bulk gravitational theory. The most well known example is the relationship between minimal surfaces in the bulk and the boundary entanglement entropy, as described by the Ryu-Takayanagi formula. Another example is measures of quantum complexity, whose bulk duals are believed to be a class of geometric bulk observables called ``complexity=anything'' that we explain in the main body of the thesis. In this thesis, we study these holographic quantum information probes in two families of geometries that arise either in AdS/CFT or in related string-theory derived dualities. We explore the two families of geometries for essentially different purposes. First, we consider so-called shell geometries, which are sourced by a spherical distribution of Dp-branes. We are interested in these geometries as they contain within the shell a region of flat spacetime. Hence, this setup gives us a clean way to study a region of flat spacetime geometry in a setting with a controlled holographic dual theory. Our motivation is then to use this setup to extract lessons relevant for the quest to understand holography in asymptotically flat spacetimes. To this end, we study the holographic entanglement entropy and associated entropic c-functions in these backgrounds. We also explore the properties of so-called internal RT surfaces in these geometries, and draw a connection to RT surfaces in asymptotically flat spacetimes. We also briefly evaluate a holographic complexity observable in this background, and confirm that the result is compatible with the conclusion of the entanglement entropy calculations. We conclude that the creation of the flat space region entails a drastic reduction in effective IR degrees of freedom in the boundary theory. Then, we investigate how so-called complexity=anything observables encode the interior geometry of (d+1)-dimensional asymptotically AdS black holes. The flexibility of this class of observables allows the corresponding extremal surfaces to be pushed arbitrarily close to the spacelike singularity, and we show that their late-time growth rate carries information about the near-singularity geometry. After resolving a puzzle concerning codimension-one observables near the singularity, we evaluate observables defined on constant-mean-curvature slices and find that the late-time growth rate depends on the value of the mean curvature, which controls how deeply the slices probe the interior. This family of observables then encodes properties of the interior region. Comparing the uncharged and charged cases, we find that for AdS-Reissner–Nordström black holes these observables only probe the interior up to the inner horizon, so in this case the observables do not reveal the presence of a singularity.
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    Managing Extreme Events for Insurance and Finance
    (University of Waterloo, 2026-09-25) Nguyen, Minh Chau
    Insuring losses from natural perils such as hurricanes and earthquakes has traditionally been challenging to the insurance sector, partly because of their heavy-tailed nature. Due to this characteristic of the losses, the valuation of risk management methods is met with a high degree of uncertainty and critical computational costs. By using techniques involving regular variation and Extreme Value Theory (EVT), in this thesis, we propose convenient analytical approximations to key quantities of two risk management mechanisms: catastrophe risk pooling and catastrophe bonds (CAT bonds). Through the derivation of these approximations, we aim at compensating computational limitations arising from the analysis of extreme events as well as providing useful insights for practical implementations. The first focus of this thesis is on optimizing a structure of catastrophe risk pool so that participants can attain a Pareto optimal diversification benefit from joining the pool. Determining the practical optimal pool entails solving a high-dimensional optimization problem, for which analytical solutions are typically unavailable and numerical methods can be computationally intensive and potentially unreliable. To address this challenge, we evaluate the diversification benefit in the limit and use the result to derive an asymptotically optimal pool as an approximation to the practical optimal pool, and a canonical pool as a benchmark. Through numerical studies, we show that the proposed pools provide accurate and reliable approximations to the practical optimal pool. We also conduct an empirical analysis using data from the U.S. National Flood Insurance Program (NFIP) to illustrate the relatively straightforward implementation of this framework. The second focus of this thesis is on constructing a catastrophe risk pool by considering three objectives: optimal diversification benefits for participants, social equity through equal benefits, and premiums which are mindful of both the pool’s solvency and participants’ benefits. Each design requirement can be expressed as an optimization problem with respect to the participants’ losses covered by the pool and the loadings they pay on top of the fair charge. We investigate a benchmark flexible pooling scheme and a truncated pooling scheme. For each scheme, optimal solutions for each problem are derived and compared using insights from EVT. We then combine the results and propose under each pooling scheme a balanced pooling design which can potentially balance the three objectives. We observe that the balanced pools under the two pooling structures asymptotically coincide in the limit case, and a weaker tail dependence between participants’ losses would improve participants’ benefits within the balanced pools. Theoretical results are verified through a numerical study, and the implementation of the balanced pool under the truncated scheme is illustrated through an empirical analysis of the U.S. NFIP data. The third focus of this thesis is on the question of pricing a CAT bond - a financial product which allows catastrophe risk to be transferred from the insurance sector to the bond market. Despite the rapid development of the CAT bond market, the market pricing of this product proves to be challenging due to the nature of catastrophe losses, as well as since its evaluation requires using numerical methods which could be computationally demanding. By using insights from EVT and a product pricing measure previously proposed in the literature, we derive two tractable approximations to the expected maturity payment of a zero-coupon CAT bond. This value can then be discounted by an independent risk-free rate process to obtain the bond price. Four simulations are then carried out to showcase the flexibility of the framework in accommodating various loss models, especially under changing climate, as well as to verify its coherence with the dependence-free property of the expected maturity payment. The results show that our approximations are accurate, flexible, and provide a considerable reduction in computational costs. Through the analysis on these three research questions, we aim at enhancing the implementation of risk pooling and CAT bonds in practice through a rigorous application of EVT techniques, thus enriching the risk management toolbox for extreme event risk in finance and insurance.
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    A Performance-Driven, Multi-Dimensional Framework for Assessing Environmental and Functional Quality in Buildings
    (University of Waterloo, 2026-09-25) Rywak, Joanna
    Since modern humans spend over 90% of their time indoors, the majority of this time at home, understanding how residential buildings impact the environment and the building occupants is imperative in improving future design and retrofit strategies. Multi-unit residential buildings in particular represent a growing portion of Canada’s building stock and present unique challenges related to building quality. With 40% of global energy consumption represented by buildings, optimizing their design in specific typologies can reduce overall environmental impact and, in many cases, improve thermal comfort of residents. Likewise, daylight in buildings has been shown to impact occupant well-being and may also contribute to energy efficiency. One final aspect affecting indoor environmental quality that is important to occupant health is indoor air quality, which has gained increased focus with recent wildfire smoke events. This study aims to quantify the environmental quality of existing multi-unit residential buildings in the Waterloo Region through three main research objectives: 1) estimating energy performance through modelling current energy use and potential energy production; 2) developing a modelling methodology that allows for the comparison of daylight and energy performance at the unit level; and 3) measuring pollutant concentrations, temperature variations, and occupant perceptions in case study units. The three areas of focus are tied together through 93 survey results from 8 case study buildings covering resident perceptions of thermal comfort, daylight, and air quality. For the first objective, case study buildings were modelled and validated using utility data, producing estimates of current energy use, energy use after retrofit measures are implemented, and potential photovoltaic energy production. Public housing case study buildings constructed in 1960-1980 were found to have the highest energy consumption, with lower perceived thermal comfort. Overheating was identified as a concern across both public and private housing from the oldest era of construction. To address the second objective, daylight models were created of four units representing each cardinal direction of the building façade and these results were compared to the unit-level energy modelling results. 37.5% and 44.6% of the units studied did not meet the daylighting thresholds for sDA and illuminance, respectively. Balcony width and unit aspect ratio were determined to have the greatest impact on EUI through a correlation analysis. The third objective was achieved by conducting indoor air quality measurements in 8 units across 5 case study buildings and distributing a questionnaire to residents. Correlations were explored between concentrations of indoor and outdoor pollutants, temporal changes across units, and comparison with questionnaire results. Perceived indoor air quality was found to have little correlation with measured results of pollutants, highlighting the need for increased testing in units and education of building occupants. These objectives were validated using 93 survey results from 8 of the case study buildings, resulting in a cohesive analysis of various aspects of environmental quality. The new dataset of existing MURBs coupled with analyzing the impacts of energy use, daylighting, and indoor air quality on building performance allows for a better understanding of current conditions and improved design of future housing developments and retrofits.
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    Unruh-DeWitt Detectors Freely Falling into BTZ Black Holes
    (University of Waterloo, 2026-09-25) Preciado Rivas, Maria Rosa
    Understanding what an observer experiences while falling into a black hole is part of the larger problem of describing quantum phenomena in strong gravitational fields, for which no complete and generally accepted theory of quantum gravity yet exists. Even within quantum field theory in curved spacetime, the question is nontrivial because particle content is observer-dependent: what a detector registers depends on its trajectory, the state of the field, and the spacetime geometry. This calculation is particularly challenging for an infalling observer, whose trajectory is nonstationary and not adapted to the black hole's symmetries. This thesis asks what an infalling observer registers using Unruh-DeWitt detectors coupled to a quantum scalar field. We study detectors in the static and rotating Bañados-Teitelboim-Zanelli (BTZ) black holes and the RP2 geon. These spacetimes are locally anti-de Sitter in three dimensions (AdS3) and are constructed as quotients of AdS3. This construction allows us to obtain their field correlation functions from the AdS3 correlation function using the method of images, making the detector response relatively easy to calculate. Motivated by conflicting conclusions about whether an infalling detector exhibits a special feature across the horizon in Schwarzschild spacetime, we first study a detector falling into a static BTZ black hole. We find that its response remains smooth and monotonic across the event horizon. However, the transition rate, defined as the time derivative of the response function, exhibits points of nondifferentiability that we call glitches. We discuss the geometric origin of these glitches and how they are related to the global topology of the spacetime. Extending the calculation to the rotating BTZ black hole and the RP2 geon, we find that the locations and symmetries of the glitches are sensitive to both the rotational and hidden topology of the spacetime. Both modifications of the static BTZ spacetime introduce new families of glitches and produce qualitatively different behavior in the transition rate. Finally, motivated by previous work in Schwarzschild spacetime, we define an effective temperature by comparing the infalling response to that of a geodesic detector in a thermal AdS3 state of known temperature. This effective temperature increases smoothly during infall, remains finite at the event horizon, and is nearly independent of the detector gap over the range studied. Our results extend the effective temperature prescription to a different black hole geometry, showing that the principal qualitative features found in Schwarzschild black holes persist in BTZ black holes. This thesis provides a partial answer to the guiding question of what an observer perceives while falling into a black hole, using Unruh-DeWitt detectors: an infalling detector need not register a special feature at the event horizon; still, its transition rate can reveal the global structure of the spacetime, and its transition function allows for the estimation of an effective temperature.