Exotic quantum systems -- those with macroscopic quantum behavior with no classical analogue -- have been a mainstay of condensed matter theory since the discovery of the quantum Hall effect. Since then, several families of related systems have been uncovered. Some, such as topological insulators, were predicted first and found experimentally later. Others are more elusive, like strongly correlated bosonic symmetry protected topological phases in high dimension, of which concrete evidence is still lacking. In this dissertation, we study several examples of exotic quantum systems. For SPT phases, we present a physically motivated classification scheme for interacting bosons and a bulk signature independent of boundary. We then construct a new, beyond Landau-Ginzburg second-order phase transition between two ordered phases of the Heisenberg magnet on the triangular lattice. Finally, we investigate an infinite family of spin liquid states, and conjecture on their connection to black holes.

Advanced nuclear fuel cycles are dependent on successful chemical separation of various elements present in the used fuel. Numerous solvent extraction systems have been developed for this purpose. In these solvent extraction systems, aggregation phenomena can interfere with the efficiencies of the processes and decrease the successfulness of the separation. The predictability of these phenomena have been challenging due to the lack of a fundamental understanding of the mechanism that drives these aggregate formations. Previous research has shown that these aggregates may be linked to a synergistic effect, whereby the extraction of metal ion into the organic phase is enhanced with mixtures of extraction reagents compared to each reagent used alone. To investigate the aggregation more closely and to probe the possibility of a link between aggregation and synergy, combined solutions of tri-n-butyl phosphate (TBP) and dibutyl phosphoric acid (HDBP) in n-dodecane were chosen as the organic phase to be contacted with an aqueous phase containing a single metal ion from the lanthanide series in nitric acid. Distribution ratios of the metal ions between the phases as well as water uptake and nitric acid extraction into the organic phase were used to investigate this aggregation phenomenon more closely and to understand the extraction behavior of this binary extractant system. Additionally, X-ray and neutron scattering and X-ray absorption techniques were used to investigate the macromolecular phase behaviors of the organic phase, with scattering yielding information regarding aggregate size and shape and absorption yielding information on the complex environment of the extracted metal ions. The combination of these techniques provide a more complete picture of the organic phase and may shed light on the link to synergy and mixed complexes. Our studies show that the complexes resulting from extraction of lanthanides into TBP:HDBP system differ from those that have been previously explored in these types of systems. This finding coupled with the formation of elongated rod-like aggregate structures formed in the organic phase may suggest that the complexes formed by the extraction of lanthanides by TBP:HDBP may be incorporated into the micellar structures and indicate a link between synergy and aggregate formation.

This dissertation contains three essays on the relationship between the spatial distribution of economic activity and different types of public goods. In the first essay, I study how changes in transport infrastructure affect the location decisions of firms by examining how manufacturers responded to changes in road quality in Indonesia. Using new data, I document massive upgrades to Indonesia's highway networks during the 1990s, a period in which national transportation funding increased by 83 percent. I first show that these road improvements were accompanied by a significant dispersion of manufacturing activity, and that different industries responded in ways predicted by theory. To make better counterfactual predictions, I develop a structural model of location choice in which firms face a trade off: locating closer to demand sources requires firms to pay higher factor prices. The model predicts that some location characteristics relevant to firms are determined in equilibrium, necessitating the use of instrumental variables. I estimate a random coefficients logit model with endogenous choice characteristics and find significant differences in firms' willingness to pay for greater market access across different industrial sectors. Counterfactual policy simulations suggest that new toll roads connecting urban areas would cause a modest amount of industrial suburbanization. In contrast, upgrading rural roads would have little or no effect on equilibrium firm locations.

In the second essay, co-authored with Bryan Graham, we provide estimates of the implicit prices that consumers and firms pay for access to infrastructure in Honduras. Without credible estimates of the welfare effects of infrastructure improvements, it is impossible for policymakers to know whether the benefits of these investments outweigh their substantial costs. A major challenge with trying to understanding the welfare consequences of improved transport infrastructure is an identification problem: transport improvements are never randomly assigned. We overcome this identification program by exploiting variation from a novel natural experiment: Honduras' infestation with Panama disease. The Honduran railroad network was constructed by fruit companies to ship bananas from plantations to port cities, but because of an unpredictable outbreak of Panama disease, major plantations and their associated railway infrastructure were abandoned. We argue that outbreaks of Panama disease were extremely difficult to predict, and because of this, conditional on the railway network that existed in the 1930s and a host of observable characteristics, the areas where railway lines were abandoned were randomly assigned. We use our identification strategy to uncover the implicit prices of access to infrastructure paid by consumers and the implicit production costs paid by firms.

In the third essay, co-authored with Rachel Glennerster and Edward Miguel, we study how spatial variation in ethnic diversity, which exists largely for historical reasons, affects the provision of local public goods in rural Sierra Leone. Scholars have pointed to ethnic divisions as a leading cause of underdevelopment, due in part to their adverse effects on public goods. We investigate this issue in post-war Sierra Leone, one of the world's poorest countries. To address concerns over endogenous local ethnic composition, we use an instrumental variables strategy relying on historical census data on ethnic composition. We find that local diversity is not associated with worse public goods provision across a variety of outcomes, specifications, and diversity measures, with precisely estimated zeros. We investigate the role that leading mechanisms proposed in the literature play in generating the findings.

Chapter one provides a summary of efforts towards the syntheses of the welwitindolinones with bicyclo[4.3.1]decane cores. Emphasis is given to more recent approaches that have successfully assembled the bicyclic core of the natural products. Chapters two and three are a discussion of our studies relating to a model system of the welwitindolinone natural products. Chapter two focuses on the use of an aryne cyclization to assemble the bicyclo[4.3.1]decane framework of the welwitindolinones. Chapter three covers initial attempts to install the bridgehead nitrogen substituent present in the natural products in addition to the synthesis of a functionalized aryne cyclization substrate.

Chapters four and five present our total syntheses of the welwitindolinone natural products. The enantiospecific total syntheses of N-methylwelwitindolinone C isothiocyanate, N-methylwelwitindolinone C isonitrile, 3-hydroxy-N-methylwelwitindolinone C isothiocyanate and 3-hydroxy-N-methylwelwitindolinone C isonitrile are detailed. The approach to these natural products features an aryne cyclization to construct the bicyclo[4.3.1]decane core of the molecules as well as a late-stage nitrene insertion reaction to install the bridgehead nitrogen substituent. The use of a deuterium kinetic isotope effect to improve the yield of the nitrene insertion is also presented. In addition, a computational method to predict the stereochemistry of a previously unconfirmed stereocenter in the hydroxylated natural products as well as experimental validation of the computational findings is discussed.

Hepatocellular carcinoma is the sixth most common cancer worldwide and the leading cause of death among patients with cirrhosis. The vast majority of these patients have the unresectable, intermediate-stage form of the disease, for which the standard of care is transarterial chemoembolization. With the health care sector rapidly outgrowing the national economy, maximizing value is now a major priority in health policy, especially with regard to cancer. Recent evidence suggests that stereotactic body radiotherapy may be a viable alternative to transarterial chemoembolization among patients of in early or very early stage of carcinoma. This evidence warrants a cost-effectiveness analysis, which not been conducted to date; the results of this study may directly impact practice guidelines for this disease. A Markov decision model was used to model the clinical trajectory of a typical patient with unresectable hepatocellular carcinoma. Costs were derived from a combination of previous studies and economic outcomes data. We hypothesized that stereotactic body radiotherapy achieves significantly greater cost-effectiveness than the current standard of care for hepatocellular carcinoma but we found the opposite may be in fact true and that transarterial chemoembolization may a more efficient management strategy for typical patients with unresectable hepatocellular carcinoma.