“Hypnotic.… [Langlands] begins to see not just the beauty of an object.… but the deeper purpose for which each has been created.” —New York Times Faced with an endless supply of mass-manufactured products, we find ourselves nostalgic for goods bearing the mark of authenticity—hand-made tools, local brews, and other objects produced by human hands. Archaeologist and medieval historian Alexander Langlands reaches as far back as the Neolithic period to recover our lost sense of craft, combining deep history with detailed scientific analyses and his own experiences making traditional crafts. Craft brims with vivid storytelling, rich descriptions of natural landscape, and delightful surprises that will convince us to introduce more craft into our lives.
During World War Two Britain had to look to the land to provide the produce it had previously shipped in from abroad, meaning huge changes on both the agricultural and domestic scenes. Accompanying an 8-part BBC series and written by the three presenters who spend a year living on a reconstructed farm from the era, Wartime Farm sets these changes within a historical context and looks at the day-to-day life of that time. Exploring a fascinating chapter in Britain's recent history, we see how our predecessors lived and thrived in difficult conditions with extreme frugality and ingenuity. From growing your own vegetables and keeping chickens in the back yard, to having to 'make do and mend', many of the challenges faced by wartime Britons have resonance today. Fascinating historical detail and atmospheric story-telling make this a truly compelling read.
The Ancient Ways of Wessex tells the story of Wessex’s roads in the early medieval period, at the point at which they first emerge in the historical record. This is the age of the Anglo-Saxons and an era that witnessed the rise of a kingdom that was taken to the very brink of defeat by the Viking invasions of the ninth century. It is a period that goes on to become one within which we can trace the beginnings of the political entity we have come to know today as England. In a series of ten detailed case studies the reader is invited to consider historical and archaeological evidence, alongside topographic information and ancient place-names, in the reconstruction of the networks of routeways and communications that served the people and places of the Anglo-Saxon kingdom of Wessex. Whether you were a peasant, pilgrim, drover, trader, warrior, bishop, king or queen, travel would have been fundamental to life in the early middle ages and this book explores the physical means by which the landscape was constituted to facilitate and improve the movement of people, goods and ideas from the seventh through to the eleventh centuries. What emerges is a dynamic web of interconnecting routeways serving multiple functions and one, perhaps, even busier than that in our own working countryside. A narrative of transition, one of both of continuity and change, provides a fresh and alternative window into the everyday workings of an early medieval landscape through the pathways trodden over a millennium ago.
The Ancient Ways of Wessex tells the story of Wessex’s roads in the early medieval period, at the point at which they first emerge in the historical record. This is the age of the Anglo-Saxons and an era that witnessed the rise of a kingdom that was taken to the very brink of defeat by the Viking invasions of the ninth century. It is a period that goes on to become one within which we can trace the beginnings of the political entity we have come to know today as England. In a series of ten detailed case studies the reader is invited to consider historical and archaeological evidence, alongside topographic information and ancient place-names, in the reconstruction of the networks of routeways and communications that served the people and places of the Anglo-Saxon kingdom of Wessex. Whether you were a peasant, pilgrim, drover, trader, warrior, bishop, king or queen, travel would have been fundamental to life in the early middle ages and this book explores the physical means by which the landscape was constituted to facilitate and improve the movement of people, goods and ideas from the seventh through to the eleventh centuries. What emerges is a dynamic web of interconnecting routeways serving multiple functions and one, perhaps, even busier than that in our own working countryside. A narrative of transition, one of both of continuity and change, provides a fresh and alternative window into the everyday workings of an early medieval landscape through the pathways trodden over a millennium ago.
This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.
This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.
The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.
Ever since 1911, the Solvay Conferences have shaped modern physics. The 23rd edition, chaired by 2004 Nobel Laureate David Gross, did not break with that tradition. It gathered most of the leading figures working on the central problem of reconciling EinsteinOCOs theory of gravity with quantum mechanics. These proceedings give a broad overview with unique insight into the most fundamental issues raised by this challenge for 21st century physics, by distinguished renowned scientists. The contributions cover: the status of quantum mechanics, spacetime singularities and breakdown of classical space and time, mathematical structures underlying the most promising attempts under current development, spacetime as an emergent concept, as well as cosmology and the cosmological constant puzzle. A historical overview of the Solvay conferences by historian of sciences Peter Galison opens the volume. In the Solvay tradition, the volume also includes the discussions among the participants OCo many of which were quite lively and illustrate dramatically divergent points of view OCo carefully edited and reproduced in full.
Alexander Baumgarten's Ethica Philosophica (1740) served as a chief textbook of philosophical instruction in German universities for several decades, and was used by Immanuel Kant for his lectures on moral philosophy between 1759 and 1794. Now translated into English for the first time, John Hymers explores the extent of Baumgarten's influence on the development of German philosophy. Accompanied by an introduction to Baumgarten and his work, this translation features an explanation of the main themes of the Ethica Philosophica, touching upon its relation to Christian Wolff and G.F. Meier's practical philosophy, but focusing especially on its role in Kant's lectures. First-time translations of elucidatory passages from the writings of Meier, Wolff, and Heinrich Köhler appear together with the relevant transcriptions of Kant's lectures on ethics. Based on a thorough knowledge of the original text, Hymers' clear translation and supporting material makes it possible to distinguish Kant's own remarks and insights from his attempts to expound and summarize Baumgarten's ideas. This is a much-needed contribution for anyone working in the history of modern philosophy.
This proceedings volume is devoted to a wide variety of items, both in theory and experiment, of particle physics such as tests of the Standard Model and beyond, physics at the future accelerators, neutrino and astroparticle physics, heavy quark physics, non-perturbative QCD, quantum gravity effects and cosmology. It is important that the papers in this volume reveal the present status and new developments in the above-mentioned items on the eve of a new era that starts with the Large Hadron Collider (LHC).
First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.
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