Realising formal groups

We show that a large class of formal groups can be realised functorially by even periodic ring spectra. The main advance is in the construction of morphisms, not of objects.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-8.abs.htm

Proofs of God in Early Modern Europe

Proofs of God in Early Modern Europe offers a fascinating window into early modern efforts to prove God’s existence. Assembled here are twenty-two key texts, many translated into English for the first time, which illustrate the variety of arguments that philosophers of the seventeenth and eighteenth centuries offered for God. These selections feature traditional proofs—such as various ontological, cosmological, and design arguments—but also introduce more exotic proofs, such as the argument from eternal truths, the argument from universal aseity, and the argument ex consensu gentium. Drawn from the work of eighteen philosophers, this book includes both canonical figures (such as Descartes, Spinoza, Newton, Leibniz, Locke, and Berkeley) and noncanonical thinkers (such as Norris, Fontenelle, Voltaire, Wolff, Du Châtelet, and Maupertuis). Lloyd Strickland provides fresh translations of all selections not originally written in English and updates the spelling and grammar of those that were. Each selection is prefaced by a lengthy headnote, giving a biographical account of its author, an analysis of the main argument(s), and important details about the historical context. Strickland’s introductory essay provides further context, focusing on the various reasons that led so many thinkers of early modernity to develop proofs of God’s existence. Proofs of God is perfect for both students and scholars of early modern philosophy and philosophy of religion

Against the Lord's anointed: aspects of warfare and baronial rebellion in England and Normandy 1075-1265

Within a framework of arbitrary, monarchical government, baronial rebellion formed one of the principal means both of expressing political discontent and of seeking the redress of grievances. So frequent were its manifestations that hostilities arising from armed opposition to the crown account for a large proportion of warfare waged in England, Normandy and the continental Angevin lands in the eleventh and twelfth centuries. The subject of revolt, lying as it does close to the heart of crownbaronial interaction, is as fundamental as it is multifaceted, embracing many issues of central importance, for example the legal status of revolt and its complex relationship with concepts of treason; the nature of homage and fealty, and the question of the revocability of these bonds in relation to the king; the growth in notions of the crown, of maiestas and the influence of Roman Law; political theories of resistance and obedience; the limitations imposed by ties of kinship and of political sympathy among the baronage on the king's ability to suppress revolt and to enforce effective punishment; and the extent of the king's logistical and military superiority

The chromo-weibel instability

I discuss the physics of non-Abelian plasmas which are locally anisotropic in momentum space. Such momentum-space anisotropies are generated by the rapid longitudinal expansion of the matter created in the first 1 fm/c of an ultrarelativistic heavy ion collision. In contrast to locally isotropic plasmas anisotropic plasmas have a spectrum of soft unstable modes which are characterized by exponential growth of transverse chromo-magnetic/-electric fields at short times. This instability is the QCD analogue of the Weibel instability of QED. Parametrically the chromo-Weibel instability provides the fastest method for generation of soft background fields and dominates the short-time dynamics of the system. The existence of the chromo-Weibel instability has been proven using diagrammatic methods, transport theory, and numerical solution of classical Yang-Mills fields. I review the results obtained from each of these methods and discuss the numerical techniques which are being used to determine the late-time behavior of plasmas subject to a chromo-Weibel instability

The chromo-Weibel instability

I discuss the physics of non-Abelian plasmas which are locally anisotropic in momentum space. Such momentum-space anisotropies are generated by the rapid longitudinal expansion of the matter created in the first 1 fm/c of an ultrarelativistic heavy ion collision. In contrast to locally isotropic plasmas anisotropic plasmas have a spectrum of soft unstable modes which are characterized by exponential growth of transverse chromo-magnetic/-electric fields at short times. This instability is the QCD analogue of the Weibel instability of QED. Parametrically the chromo-Weibel instability provides the fastest method for generation of soft background fields and dominates the short-time dynamics of the system. The existence of the chromo-Weibel instability has been proven using diagrammatic methods, transport theory, and numerical solution of classical Yang-Mills fields. I review the results obtained from each of these methods and discuss the numerical techniques which are being used to determine the late-time behavior of plasmas subject to a chromo-Weibel instability.Comment: 5 pages, 4 figures; v2 one reference added, small changes to text; Proceedings contribution for the International Symposium on Multiparticle Dynamics, Paraty, Rio de Janeiro, Brazil, Sept 2-8, 2006; Invited tal