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This thesis studies the geometry of objects from 2-dimensional statistical physics in the continuum. Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, conformally invariant random curves with a domain-Markov property. The family is indexed by a parameter, usually denoted by κ, which controls the regularity of the curve. We give the definition of the SLEκ process, and summarise the proofs of some of its properties. We give particular attention to the Rohde-Schramm theorem which, in broad terms, tells us that an SLEκ is a curve. In Chapter 2 we introduce the Gaussian free field (GFF), a conformally invariant random surface with a domain-Markov property. We explain how to couple the GFF and an SLEκ process, in particular how a GFF can be unzipped along a reverse SLEκ to produce another GFF. We also look at how the GFF is used to define Liouville quantum gravity (LQG) surfaces, and how thick points of the GFF relate to the quantum gravity measure. Chapter 3 introduces a diffusion on LQG surfaces, the Liouville Brownian motion (LBM). The main goal of the chapter is to complete an estimate given by N. Berestycki, which gives an upper bound for the Hausdor dimension of times that a γ-LBM spends in α-thick points for γ, α ∈ [0, 2). We prove the corresponding, tight, lower bound. In Chapter 4 we give a new proof of the Rohde-Schramm theorem (which tells us that an SLEκ is a curve), which is valid for all values of κ except κ = 8. Our proof uses the coupling of the reverse SLEκ with the free boundary GFF to bound the derivative of the inverse of the Loewner flow close to the origin. Our knowledge of the structure of the GFF lets us find bounds which are tight enough to ensure continuity of the SLEκ trace.

The purpose of this descriptive study was to understand whether a relationship exists between an individual's behavioral intention to use a Bible-based chatbot that leverages AI to create human-like engagement with Scripture and the constructs of performance expectancy, effort expectancy, perceived enjoyment, and perceived risk, controlling for gender, age, and experience among registered users of the Inductive Bible Study App. Data was collected through an online survey and analyzed using Partial Least Squares Structural Equation Modeling (PLS-SEM), multi-group analysis (MGA), and homogeneity-of-slopes analysis of covariance (ANCOVA). While this quantitative descriptive study validated the correlation between each of the four reflective constructs and the formative construct (behavioral intent), the data suggests that perceived enjoyment maintains the strongest link to behavioral intent. In addition, the moderators appear to indicate that the strongest correlation to behavioral intent is found in communities of younger males with no prior exposure to chatbots. The results of this study provide useful insights into how individuals perceive and make decisions about using technology for religious or spiritual purposes, and how these perceptions may differ based on demographic factors. Additionally, the results inform the development and implementation of similar AI-based tools in religious or spiritual contexts and provide insights into how leaders in these contexts can effectively utilize technology to engage with their communities.