Differential forms, Fukaya A∞A_\infty algebras, and Gromov-Witten axioms

Consider the differential forms $A^*(L)$ on a Lagrangian submanifold $L \subset X$. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved $A_\infty$ structures on $A^*(L),$ parameterized by the cohomology of $X$ relative to $L.$ The family of $A_\infty$ structures satisfies properties analogous to the axioms of Gromov-Witten theory. Our construction is canonical up to $A_\infty$ pseudoisotopy. We work in the situation that moduli spaces are regular and boundary evaluation maps are submersions, and thus we do not use the theory of the virtual fundamental class.Comment: 51 pages, 6 figures; improved exposition, added illustrations, corrected minor errors, added reference

The Supreme Court’s Theory of Private Law

In this Article, we revisit the clash between private law and the First Amendment in the Supreme Court\u27s recent case, Snyder v. Phelps, using a private-law lens. We are scholars who write about private law as individual justice, a perspective that has been lost in recent years but is currently enjoying something of a revival. Our argument is that the Supreme Court\u27s theory of private law has led it down a path that has distorted its doctrine in several areas, including the First Amendment–tort clash in Snyder. In areas that range from punitive damages to preemption, the Supreme Court has adopted a particular and dominant, but highly contested, theory of private law. It is the theory that private law is not private at all; it is part and parcel of government regulation, or public law in disguise. Part I is a brief overview of how that jurisprudential view came to be, as well as a sketch of a competing view of private law as individual justice. In Part II, we briefly trace the development of the doctrine surrounding the tension between the First Amendment and private law, particularly tort law, and how it helps lead to the view of private law as government regulation displayed in Snyder. We also point out how the intentional infliction of emotional distress tort, the main claim at issue in Snyder, is a particularly poor vehicle for the Court\u27s theory of private law. A relatively recent tort, it was developed by scholars and judges as a means of redress for plaintiffs who had been wronged, but were left without a remedy. Part III presents the central claims of the Article. We argue that the conception of private law as government regulation in Snyder arises from a combination of (1) the doctrinal tools that judges use in First Amendment cases, (2) the unitary nature of the state-action doctrine, and (3) the influence of instrumentalism, specifically in obscuring the plaintiff\u27s agency and the state interest in redress, and in privileging a particular view of compensation. In Part IV, we present some normative or prescriptive implications of our analysis, and then conclude

The Supreme Court’s Theory of Private Law

In this Article, we revisit the clash between private law and the First Amendment in the Supreme Court\u27s recent case, Snyder v. Phelps, using a private-law lens. We are scholars who write about private law as individual justice, a perspective that has been lost in recent years but is currently enjoying something of a revival. Our argument is that the Supreme Court\u27s theory of private law has led it down a path that has distorted its doctrine in several areas, including the First Amendment–tort clash in Snyder. In areas that range from punitive damages to preemption, the Supreme Court has adopted a particular and dominant, but highly contested, theory of private law. It is the theory that private law is not private at all; it is part and parcel of government regulation, or public law in disguise. Part I is a brief overview of how that jurisprudential view came to be, as well as a sketch of a competing view of private law as individual justice. In Part II, we briefly trace the development of the doctrine surrounding the tension between the First Amendment and private law, particularly tort law, and how it helps lead to the view of private law as government regulation displayed in Snyder. We also point out how the intentional infliction of emotional distress tort, the main claim at issue in Snyder, is a particularly poor vehicle for the Court\u27s theory of private law. A relatively recent tort, it was developed by scholars and judges as a means of redress for plaintiffs who had been wronged, but were left without a remedy. Part III presents the central claims of the Article. We argue that the conception of private law as government regulation in Snyder arises from a combination of (1) the doctrinal tools that judges use in First Amendment cases, (2) the unitary nature of the state-action doctrine, and (3) the influence of instrumentalism, specifically in obscuring the plaintiff\u27s agency and the state interest in redress, and in privileging a particular view of compensation. In Part IV, we present some normative or prescriptive implications of our analysis, and then conclude

Mass Loss by Hot Stars

Mechanism explaining mass loss for luminous hot stars using ultraviolet line spectra of some ion

One Hour of Chemical Demonstrations

This article describes a diverse set of chemistry demonstrations especially selected to encourage student interaction and to be easily transported. The demonstrations may be presented at a level that can be tailored to any audience– from very young children to high school students planning careers in science. An ideal environment is a small classroom with 20-30 students where everyone can take part in the discussion. Once the chemicals are prepared, the collection of demonstrations takes about ten minutes to set-up, and one hour (or less) to perform. Very little is needed at the visiting site, no more than a table and a pitcher of water. A single electrical outlet is useful, but not essential. In Table 2 th