Doctor of Philosophy

dissertationThis dissertation reports the work I have completed with two research projects, using paleoecological methods to compare precipitation histories to inform archaeological investigation at two sites. The first chapter will present an analysis of the population history of leporids (rabbits and hares) from Abrigo de los Escorpiones, a shell midden site on the coast of northern Baja California, over the past 10,000 years. Comparison of that population history to sedimentary-based records of the frequency and intensity of El Niño events over the same time period reveals strong correlations between precipitation and overall abundance, taxonomic composition, and age structure of the leporid population at the site. The second chapter of this dissertation reports the results of a multiproxy paleoenvironmental reconstruction of climate during the past 2000 years at a site in Range Creek Canyon, in the Tavaputs Plateau region of eastern Utah. Results from the analysis of fossil pollen, macroscopic charcoal, sediment loss on ignition, magnetic susceptibility, and stable carbon isotope analysis of sediments demonstrate the site was used by human horticulturalists as a maize field during the Fremont occupation of the canyon between roughly AD 800 and AD 1100. Additionally, the paleoenvironmental proxies reveal the period of Fremont occupation of the canyon likely saw less summer precipitation than today, very likely necessitating irrigation of fields for maize horticulturalists

Properties expressible in small fragments of the theory of the hyperfinite II_1 factor

We show that any II$_1$ factor that has the same 4-quantifier theory as the hyperfinite II$_1$ factor $\mathcal{R}$ satisfies the conclusion of the Popa Factorial Commutant Embedding Problem (FCEP) and has the Brown property. These results improve recent results proving the same conclusions under the stronger assumption that the factor is actually elementarily equivalent to $\mathcal{R}$. In the same spirit, we improve a recent result of the first-named author, who showed that if (1) the amalgamated free product of embeddable factors over a property (T) base is once again embeddable, and (2) $\mathcal{R}$ is an infinitely generic embeddable factor, then the FCEP is true of all property (T) factors. In this paper, it is shown that item (2) can be weakened to assume that $\mathcal{R}$ has the same 3-quantifier theory as an infinitely generic embeddable factor.Comment: 13 pages. First draft; comments welcome

A survey on the model theory of tracial von Neumann algebras

We survey the developments in the model theory of tracial von Neumann algebras that have taken place in the last fifteen years. We discuss the appropriate first-order language for axiomatizing this class as well as the subclass of II$_1$ factors. We discuss how model-theoretic ideas were used to settle a variety of questions around isomorphism of ultrapowers of tracial von Neumann algebras with respect to different ultrafilters before moving on to more model-theoretic concerns, such as theories of II$_1$ factors and existentially closed II$_1$ factors. We conclude with two recent applications of model-theoretic ideas to questions around relative commutants.Comment: 27 pages; first draft; comments welcome; to appear in the volume "Model theory of operator algebras" as part of DeGruyter's Logic and its Application Serie