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`Cosmic Noon' is an epoch spanning $\sim$2--6 billion years after the Big Bang when galaxies are undergoing rapid star formation, morphological evolution, gaining mass and ejecting significant amounts of gas. Strong gravitational lensing by massive foreground galaxies enables detailed studies of the kinematic and morphological properties of galaxies during their crucial formative epochs at cosmic noon. This thesis focuses on studying galactic outflows of gas using strong gravitationally lensed galaxies.Outflows play the crucial role of regulating the galaxy growth by modulating the amount of gas available in a galaxy's interstellar medium at any time. However, fundamental questions about galactic outflows remain unconstrained for galaxies during this epoch. Physical properties such as the velocity at which gas is launched in outflows, the amount of mass lost via these outflows, and the fate of the ejected gas are highly uncertain.Establishing these properties will markedly improve our current understanding of how feedback processes regulate galaxy formation and evolution.This thesis represents significant progress toward establishing these quantities in galaxies at cosmic noon.The three projects presented in this thesis describe the methodology to identify and spectroscopically confirm the lensed nature of a large sample of newly discovered gravitational lens systems, and conduct spectrally and spatially resolved studies utilizing the magnification from lensed galaxies to measure their outflow properties. By employing state-of-the-art semi-supervised learning techniques within a deep learning architecture and utilizing a training dataset containing both simulated lenses and non-lensed survey images, I demonstrated that we can greatly reduce the human effort required to find lensed candidates from imaging surveys. These machine learning methods dedicated to identifying lensed candidates exhibit remarkable effectiveness, achieving a success rate of $\sim$90\%.I studied a sample of 20 lensed galaxies with good spectral resolution to characterize the kinematic structure of outflows at cosmic noon, finding good agreement with predictions for momentum-driven outflows.These observations confirm that galaxies at this epoch launch powerful, fast, metal-enriched outflows ubiquitously during their formative stages.I also performed a spatially resolved pilot study of the outflows in one lensed galaxy, which showed that the rates of mass loss due to these outflows are comparable to star formation rates. This suggests efficient coupling between stellar feedback and the driving of outflowing mass in galaxies at cosmic noon.Much of the ejected gas from these outflows, however, remains confined within the galaxy halo, indicating that outflows play a crucial role in shaping the circumgalactic medium and providing a reservoir of gas to sustain extended star formation at later times. Finally, I outline several strategies to study the impact of stellar feedback and its influence on galaxy evolution through future integral field spectroscopic observations of gravitationally lensed galaxies.

Dark matter makes up roughly 85 percent of the mass budget of the Universe. Though we cannot see it, hence the name, the formation and behavior of structures from the largest cosmological scales down to sub-galactic scales betray the existence of dark matter via its gravitational interactions. The widely accepted view of cosmological history, informed by observations of hierarchical structure formation, posits non-relativistic dark matter particles that only interact gravitationally, known as cold dark matter (CDM). However, alternative theories of dark matter may describe small-scale observations as well or better. It is essential to test variations on CDM and differentiate between models that agree on larger scales. We can observe even completely invisible dark matter structures from the way they deflect and magnify light. This phenomenon, gravitational lensing, has been used to infer some of the tightest constraints on alternative dark matter models and grows stronger as telescopes improve and sample sizes increase.This dissertation is focused on strong gravitational lensing, when multiple images of the light source appear on the sky. Particularly, I demonstrate and evaluate a method called flux-ratio analysis, which uses bright, compact sources like quasars that are lensed into four distinct images. In these systems, the main lens is an elliptical galaxy, the mass distribution of which determines the positions and relative brightnesses of the images. Low-mass dark matter structures, called halos, associated with the main lens or along the line of sight are detectable in the additional magnification or demagnification they introduce to individual images. Discrepancies between observed flux ratios and those predicted by a smooth model of the main lens indicate the presence of perturbing halos. With a sample of many lensed quasars, we can characterize the population statistics of low-mass halos. These statistics are determined by the underlying dark matter model, thus they enable us to infer constraints on it. In Chapter 1 of this work, I provide general background information on dark matter and cosmology and detail the predictions of CDM. I then discuss the use of gravitational lensing to detect dark matter and review the history of flux-ratio analysis to put my work in the context of the field.Chapter 2 of this work contains a detailed description of my flux-ratio analysis procedure as well as constraints on warm dark matter (WDM) inferred from a sample of 14 lensed quasars. I provide background on WDM theory and describe the process of simulating low-mass halo populations that align with theoretical predictions. Then I walk through my Bayesian inference procedure and its application to infer the strongest gravitational lensing constraints on WDM to date. Lastly, I explore the context of my analysis in relation to other works that used subsets of this lens sample. I highlight the differences in between our analysis procedures and potential sources of systematic error. In Chapter 3, I investigate the addition of general third- and fourth-order multipoles to the mass model. I find that multipoles with realistic amplitudes, at least when compared to the isophotes of elliptical galaxies, can perturb flux ratios as significantly as low-mass halos. If their orientation angles are left to vary freely, joint third- and fourth-order multipoles are completely degenerate with CDM halo populations when modeling quadruply-imaged quasars. This work calls into question all previous dark matter constraints from flux-ratio analysis, including those presented in Chapter 2. However, those results are still critical to the field moving forward. Until this degeneracy is mitigated, the method and degree of inclusion of multipoles into an inference procedure will strongly impact the result. Chapter 2 explores one extreme end of this spectrum -- the exclusion of multipoles.In Chapter 4, I summarize and provide a framework for reevaluating past dark matter constraints from flux-ratio analysis. I explain how comparison between observations of lens galaxy isophotes and mass models from associated lensed arcs can provide more informative priors on multipoles in future lens models. Additionally, I forecast ways that high-resolution simulations can provide complementary prior information both regarding multipoles that may be present in galactic dark matter halos and their connection to the distribution of baryons in the galaxy. Finally, I give an overview of the increase in the sample size of strong lens systems that is expected from JWST and Euclid. Though data from these telescopes holds great potential to help us understand the nature of dark matter, we must first untangle the degeneracy between smooth model complexity and low-mass halos.

We have conducted a search for new strong gravitational lensing systems in the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys' Data Release 8. We use deep residual neural networks, building on previous work presented in Huang et al. (2020). These surveys together cover approximately one third of the sky visible from the northern hemisphere, reaching a z band AB magnitude of ~22.5. We compile a training sample that consists of known lensing systems as well as non-lenses in the Legacy Surveys and the Dark Energy Survey. After applying our trained neural networks to the survey data, we visually inspect and rank images with probabilities above a threshold. Here we present 1210 new strong lens candidates.

We have conducted a search for new strong gravitational lensing systems in the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys' Data Release 8. We use deep residual neural networks, building on previous work presented in Huang et al. (2020). These surveys together cover approximately one third of the sky visible from the northern hemisphere, reaching a z band AB magnitude of ~22.5. We compile a training sample that consists of known lensing systems as well as non-lenses in the Legacy Surveys and the Dark Energy Survey. After applying our trained neural networks to the survey data, we visually inspect and rank images with probabilities above a threshold. Here we present 1210 new strong lens candidates.

There is overwhelming evidence for a link between supermassive black holes (BHs) and their host galaxies, yet the physical mechanisms behind the connection are poorly understood. Discerning between possible co-evolutionary scenarios requires precise measurements of BH masses and host properties across cosmic time. BH mass measurements outside the local universe require bright active galactic nuclei (AGNs), but the AGN light overwhelms the light of the host, making host property measurements difficult. Further, BH mass estimates rely on the unresolvable broad emission line region (BLR), and the unknown nature of the BLR limits their precision.In this dissertation, I use a unique combination of gravitational lensing and reverberation mapping techniques to tackle both issues. First, I present a semi-supervised classification approach for identifying rare lensed quasars based solely on photometry in wide-field surveys. Lenses are powerful tools for measuring host properties, but studies are limited by the small sample size, so discovery efforts are crucial. Using this technique, I successfully discovered three new lenses in the Sloan Digital Sky Survey, with several other candidates awaiting further follow-up. This approach is flexible and can easily be modified to target specific types of lenses as well as lenses in surveys covering different portions of the sky.Next, I use a modeling framework to measure precise BH masses for seven AGNs and infer the structural and kinematic properties of the Hβ BLR. This nearly doubles the sample size of modeled BLRs, allowing for a correlation analysis between BLR properties and AGN observables that can be used to improve BH mass measurements for all AGNs. I then model Hβ, CIV, and Lyα in NGC 5548 using data from 85 Hubble Space Telescope orbits and multiple ground-based telescopes to understand the similarities and differences between the optical and UV BLRs. High-z BH mass measurements rely on UV lines, but our current understanding of the UV BLR is severely lacking, so understanding their connection is critical for decreasing high-z BH mass uncertainties. Finally, I tie the previous projects together with the most precise high-z BH mass measurement to date, using data from a 4.5 year monitoring campaign of a strongly lensed quasar at z=2.805. Accounting for gravitational time delays, the campaign exceeds 6 years in duration. Understanding the co-evolution of BHs and their hosts will require measurements of this precision at high-z, and this research demonstrates that gravitational lensing makes this level of precision obtainable.