Limits of geometries

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transform into another. We develop a general framework to describe transitions in the context that both geometries involved are represented as sub-geometries of a larger ambient geometry. Specializing to the setting of real projective geometry, we classify the geometric limits of any sub-geometry whose structure group is a symmetric subgroup of the projective general linear group. As an application, we classify all limits of three-dimensional hyperbolic geometry inside of projective geometry, finding Euclidean, Nil, and Sol geometry among the limits. We prove, however, that the other Thurston geometries, in particular $\mathbb{H}^2 \times \mathbb{R}$ and $\widetilde{\operatorname{SL}_2 \mathbb{R}}$, do not embed in any limit of hyperbolic geometry in this sense.Comment: 40 pages, 2 figures. new in v2: figure 2 added, minor edits to Sections 1,2,

Coastal Capital: Dominican Republic: Case Studies on the Economic Value of Coastal Ecosystems in the Dominican Republic

Illustrates the benefits coralline beaches, reefs, and mangroves in various parts of the country offer, including providing protection against beach erosion, habitats for fisheries, potential tourism growth in protected marine areas, and local tourism

Summary Judgment in the Shadow of Erie

This essay addresses one particular challenge to federal summary judgment practice: the possibility of a successful challenge to Rule 56 of the Federal Rules of Civil Procedure, pursuant to Erie Railroad v. Tompkins and its progeny. Part II of this essay addresses differences between summary judgment as practiced in federal courts pursuant to Federal Rule 56 and summary judgment as practiced in state courts, focusing in particular on differences in the ways the federal courts and some state courts allocate the burdens on moving and non-moving parties.Part III suggests that these differences are problematic under Erie and its progeny, and in particular under the Supreme Court’s 2001 decision in Semtek International, Inc. v. Lockheed Martin Corp. Part III looks ahead to the Erie case decided in the Supreme Court’s 2010 term and considers the possible impact of that case on Federal Rule 56.6 The essay concludes that, in light of the Supreme Court’s Erie jurisprudence, the future of uniform summary judgment practice in federal courts is at least uncertain

Ghosts of 1932: The Lost History of Estate and Gift Taxation

In 1932, the United States confronted a bleak economic landscape. Amid the financial carnage caused by the 1929 stock market crash and the ensuing Great Depression, economic activity had ground to a halt, tax revenues had plunged, and the nation’s debt had soared. The declining government revenues and soaring debt threatened both the viability of American industry and the stability of the nation’s credit rating. Congress took bold action that year, enacting a massive tax bill (“the Revenue Act of 1932”) designed to balance the federal budget without further stifling economic growth. As has been true through nearly a century of tax legislation, Congress included estate and gift taxes as a component of the Revenue Act of 1932. The architects of the 1932 estate and gift tax provisions made a number of crucial legislative choices that fateful year, implicating issues of tax policy that remain as relevant today as they were some eighty years ago. Yet, histories of American taxation typically devote frustratingly little analysis to the specific estate and gift tax provisions included in the Revenue Act of 1932. As a result, despite their continued relevance, the details of key decisions, and the motivations of those who made them, effectively have been lost to history. In this paper, I seek to reclaim this lost history of estate and gift taxation. While the ensuing analysis certainly will enable us to more fully appreciate the events of 1932 and evaluate the actions Congress took in that fateful year, my inquiry is not of mere historical interest. Rather, the choices made in 1932 have helped shape the fundamental structure of U.S. estate and gift taxation for nearly eight decades, including our modern estate and gift tax code. Accordingly, understanding the events of 1932 can help us to understand why our estate and gift taxes operate the way they do as well as help inform future debate about the optimal structure of our wealth transfer tax system

Mysticism in the Middle: The Mandorla as Interpretive Tool for Reading Meister Eckhart

The spirituality of Meister Eckhart (1260–1328) is fundamentally chiaroscuro in form and expression. This word, coming from the world of art, represents in itself the collision of clarity and brightness (chiaro) with obscurity and darkness (oscuro). In one single word we have two opposites existing side-by-side creating a tension out of which arises the transformative interplay between darkness and light. The word, chiaroscuro, therefore is also an example of a language mandorla. This is another word arising from the world of art, but in this case specifically from the world of religious art and architecture. The mandorla is the almond-shaped space that results in the overlap of two complete circles.1 It represents a middle, or in-between, space where opposites collide and “conflict-without-resolution” and arises as the “direct experience of God.”2 Meister Eckhart is both a master of the chiaroscuro and the mandorla. His spiritual art, founded on incarnatio continua, issues forth in both structure and expression through the on-going interplay between human and divine often represented in his works by the relationship between darkness and light. In this essay then I will seek to demonstrate how the mandorla can serve as an interpretive tool for reading the chiaroscuro language art of Meister Eckhart. In doing so I hope to provide readers today with a means to grapple with, and more deeply appreciate, the German Dominican’s mysticism in and of the middle. First, though, a word from the middle space