In this dissertation, we study etale correspondence of hyperbolic curves with unbounded dynamics. Mochizuki proved that over a field of characteristic 0, such curves are always Shimura curves. We explore variants of this question in positive characteristic, using graph theory, l-adic local systems, and Barsotti-Tate groups. Given a correspondence with unbounded dynamics, we construct an infinite graph with a large group of ”algebraic” automorphisms and roughly measures the ”generic dynamics” of the correspondence. We construct a specialization map to a graph representing the actual dynamics. Along the way, we formulate conjectures that etale correspondences with unbounded dynamics behave similarly to Hecke correspondences of Shimura curves. Using graph theory, we show that type (3,3) etale correspondences verify various parts of this philosophy. Key in the second half of this dissertation is a recent p-adic Langlands correspondence, due to Abe, which answers affirmatively the petites camarades conjecture of Deligne in the case of curves. This allows us the build a correspondence between rank 2 l-adic local systems with trivial determinant and Frobenius traces in Q and certain height 2, dimension 1 Barsotti-Tate groups. We formulate a conjecture on the fields of definitions of certain compatible systems of l-adic representations. Relatedly, we conjecture that the Barsotti-Tate groups over complete curves in positive characteristic may be ”algebraized” to abelian schemes.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Doctor of Philosophy (PhD) / Changing the behaviour of firms to take environmental concerns into account is seen as unlikely without effective regulations. However, corporations are increasingly keen to represent themselves as ‘green’, including those in the world’s largest manufacturing sector: the car industry. Given rising concern for the environment and environmental sustainability since the 1990s this thesis asks: what motivates car firms to actually make environmental commitments? Answering this question has implications for whether these commitments are ‘real’ and if so whether they are occurring in response to material factors (e.g. state regulations and consumer demand) versus normative factors (e.g. social attitudes and internal company strategies). In order to answer it, the thesis applies the insights of the institutional varieties of capitalism approach to the German, United States and Japanese car industries, and specific firms within them, in respect of the environmental issue of climate change from 1990 to 2004. Empirical national data is analysed, as well the environmental reporting of individual firms and interviews with key personnel. The main findings are that what leads the car industry to see environmental issues as central to their business interests hinges on the impact of differing national institutional factors. Specifically, it is a matter of whether firms have a liberal market economy (LME) as their home base, in the case of US firms, or a coordinated market economy (CME) as their home base, in the case of German and Japanese firms. US car firms react more to the material imperatives of consumer demand and state regulations. German and Japanese firms are more mindful of normative factors for their initiatives, such as social attitudes (especially for German firms) and internal company strategies (especially for Japanese firms). They have more of a partnership approach with government. Therefore, car firms have very distinct ‘lenses’ through which they see the environmental performance of the cars they produce. As such, the thesis concludes that the variety of capitalism of nations has implications not just for the type of products that economic actors such as car firms produce, and the competitive advantages they develop, but also the way they address related issues arising as a result of their activities, including environmental issues.

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 106-108).

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 1999. / Includes bibliographical references. Also available on the Internet.

The main topic of this thesis is the tropicalizations of Severi varieties, which we call tropical Severi varieties. Severi varieties are classical objects in algebraic geometry. They are parameter spaces of plane nodal curves. On the other hand, tropicalization is an operation defined in tropical geometry, which turns subvarieties of an algebraic torus into certain polyhedral objects in real vector spaces. By studying the tropicalizations, it may be possible to transform algebro-geometric problems into purely combinatorial ones. Thus, it is a natural question, “what are tropical Severi varieties?” In this thesis, we give a partial answer to this question: we obtain a description of tropical Severi varieties in terms of regular subdivisions of polygons. Given a regular subdivision of a convex lattice polygon, we construct an explicit parameter space of plane curves. This parameter space is a much simpler object than the corresponding Severi variety and it is closely related to a flat degeneration of the Severi variety, which in turn describes the tropical Severi variety. We present two applications. First, we understand G.Mikhalkin’s correspondence theorem for the degrees of Severi varieties in terms of tropical intersection theory. In particular, this provides a proof of the independence of point-configurations in the enumeration of tropical nodal curves. The second application is about Secondary fans. Secondary fans are purely combinatorial objects which parameterize all the regular subdivisions of polygons. We provide a relation between tropical Severi varieties and Secondary fans.

We compare two methods for software specification: <em>algebraic specifications</em> and automata. While algebraic specifications have been around since the 1970s and have been studied extensively, specification by automata is relatively new. Its origins are in another veteran method called <em>trace assertions</em>, which considers a software module as a set of traces, that is, a sequences of function executions. A module is specified by a set of canonical traces and an equivalence relation matching one of the canonical traces to each non-canonical trace. It has been recently shown that trace assertions is an equivalent method to specification by automata. In continuation of this work on trace assertions and automata, we study how automata compare with algebraic specifications. We prove that every specification using an automaton can be converted into an algebraic specification describing the same abstract data type. This conversion utilises a set of canonical words, representing states in the automaton. We next consider varieties of monoids as a heuristic for obtaining more concise algebraic specifications from automata. Finally, we discuss the opposite conversion of algebraic specifications into automata. We show that, while an automaton always exists for every abstract data type described by an algebraic specification, this automaton may not be finitely describable and therefore may not be considered as a viable method for software specification.

The Texas rice industry has undergone many changes over the course of the industry’s existence. Recently, high costs of production and the structure of government payments have contributed to a decreasing trend in rice acreage planted in Texas. While Texas was once the top rice producer in the United States, it now ranks fifth. Despite the fact that Texas has one of the lowest levels of production among rice producing states, it currently maintains the highest per acre yields. One of the major factors in maintaining superior yields is the development of high performance rice varieties and hybrids, which provide increased yields on fewer acres. Research institutions invest a great deal of time, effort, and money towards the development of new varieties every year. Each one of these varieties has a specific set of traits that are believed to be in high demand by producers and processors. However, during the developmental stages, scientists are uncertain as to how each new gerplasm will perform once it reaches the market. This study develops a regression model, which includes competition and the characteristics of a specific variety, to estimate the life cycle of new varieties and hybrids. In addition, simulation techniques are utilized to incorporate risk into the life cycle, providing a more robust prediction of the cumulative adoption and disadoption path. Results indicate that the life cycle of new rice varieties is becoming shorter over time. Furthermore, the length of the life cycle is directly related to a new seed’s performance, compared to other varieties on the market. Varieties that provide higher levels of performance, especially higher yields, tend to have a longer life cycle and achieve a larger market share, on average.

Flag varieties of reductive Lie groups and their subvarieties play a central role in representation theory. In the early 1980s, V. Deodhar introduced a decomposition of the flag variety which was then used to study the Kazdan-Lusztig polynomials. A Deodhar-type decomposition of the product of the flag variety with itself, referred to as the double flag variety, was introduced in 2007 by B. Webster and M. Yakimov, and each piece of the decomposition was shown to be coisotropic with respect to a naturally defined Poisson structure on the double flag variety. The work of Webster and Yakimov was partially motivated by the theory of cluster algebras in which Poisson structures play an important role. The Deodhar decomposition of the flag variety is better understood in terms of a cell decomposition of Bott-Samelson varieties, which are resolutions of Schubert varieties inside the flag variety. In the thesis, double Bott-Samelson varieties were introduced and cell decompositions of a Bott-Samelson variety were constructed using shuffles. When the sequences of simple reflections defining the double Bott-Samelson variety are reduced, the Deodhar-type decomposition on the double flag variety defined by Webster and Yakimov was recovered. A naturally defined Poisson structure on the double Bott-Samelson variety was also studied in the thesis, and each cell in the cell decomposition was shown to be coisotropic. For the cells that are Poisson, coordinates on the cells were also constructed and were shown to be log-canonical for the Poisson structure. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy