It\u27s Time for a Good Hard Look in the Mirror: The Corporate Law Example

This Article asserts that the move from the industrial age to the information age represents a fundamental change to our society on such a widespread basis that the legal order must reexamine the premises about how our society functions, assessing whether foundational elements of U.S. Common Law remain valid. This Article first confronts briefly the continuing acceptance of certain foundational premises in contract and intellectual property law, illustrating that such premises are no longer supported by the realities of modern society. With fundamental change challenging multiple areas of law in the information age, this problem is worthy of widespread inquiry by legal scholars in various fields. This Article then turns to a detailed analysis of the premises supporting shareholder primacy in corporate law, demonstrating that the historic justifications for allocations of ownership, control and duties no longer support these premises. Based on the relative needs of today’s businesses vis-à-vis the contributions of various other constituencies, this Article asserts that employees should also have certain duties owed to them. This Article concludes with a novel model for creating such a stake in the form of a springing right to profit sharing

Matrix geometries and fuzzy spaces as finite spectral triples

A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy spaces defined as real spectral triples. Fuzzy 2-spheres are investigated in detail, and it is shown that the fuzzy analogues correspond to two spinor fields on the commutative sphere. In some cases it is necessary to add a mass mixing matrix to the commutative Dirac operator to get a precise agreement for the eigenvalues.Comment: 39 pages, final versio

Free Speech Has Gotten Very Expensive: Rethinking Political Speech Regulation in a Post-Truth World

(Excerpt) Protecting free speech has been a foundational principle of American democracy since the nation’s founding. A core element of free speech has long been a prohibition on regulating political speech. The principle behind this protection holds that citizens are free to make whatever political pronouncements they wish and that their speech shall remain free from government suppression. Even within the limited exceptions to unfettered political speech, like defamation or libel, the speech is not banned but may merely result in liability. A premise underlying this view is that competing viewpoints, by being made available to us all, will allow the best ideas to emerge and for truth to prevail over falsehood. Even though such an approach may be imperfect at times, the historic view holds that the risks associated with regulating political speech are far worse: allowing the government and those in power to suppress dissenting voices and thereby consolidate power

Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers

We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum for the Navier-Stokes equation and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian of the model, we prove the existence of a global-in-time weak solution to the coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the absence of a body force, the weak solution decays exponentially in time to the equilibrium solution, at a rate that is independent of the choice of the initial datum and of the centre-of-mass diffusion coefficient.Comment: 75 page

An algebraic interpretation of the Wheeler-DeWitt equation

We make a direct connection between the construction of three dimensional topological state sums from tensor categories and three dimensional quantum gravity by noting that the discrete version of the Wheeler-DeWitt equation is exactly the pentagon for the associator of the tensor category, the Biedenharn-Elliott identity. A crucial role is played by an asymptotic formula relating 6j-symbols to rotation matrices given by Edmonds.Comment: 10 pages, amstex, uses epsf.tex. New version has improved presentatio