This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.
Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
This special volume is dedicated to the memory of Andrey A. Bolibrukh. It contains two expository articles devoted to some aspects of Bolibrukh's work, followed by ten refereed research articles. Topics cover complex linear and nonlinear differential equations as well as quantum groups: monodromy, Fuchsian linear systems, Riemann-Hilbert problem, differential Galois theory, differential algebraic groups, multisummability, isomonodromy, Painlevé equations, Schlesinger equations, integrable systems, KZ equations, complex reflection groups, root systems.
We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category of polarized twistor D-modules and show a Decomposition Theorem in this category = Nous montrons un théorème de décomposition pour l'image directe d'un système local irréductible sur une variété projective complexe lisse par un morphisme à valeurs dans une autre variété projective complexe lisse. À cet effet, nous construisons une catégorie de Dmodules avec structure de twisteur polarisée et nous montrons un théorème de décomposition dans cette catégorie.
This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.
Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.
A beautiful volume that brings to light the forgotten Le Nain brothers, a trio of 17th-century French master painters who specialized in portraiture, religious subjects, and scenes of everyday peasant life In France in the 17th century, the brothers Antoine (c. 1598-1648), Louis (c. 1600/1605-1648), and Mathieu (1607-1677) Le Nain painted images of everyday life for which they became posthumously famous. They are celebrated for their depictions of middle-class leisure activities, and particularly for their representations of peasant families, who gaze out at the viewer. The uncompromising naturalism of these compositions, along with their oddly suspended action, imparts a sense of dignity to their subjects. Featuring more than sixty paintings highlighting the artists' full range of production, including altarpieces, private devotional paintings, portraits, and the poignant images of peasants for which the brothers are best known, this generously illustrated volume presents new research concerning the authorship, dating, and meaning of the works by well-known scholars in the field. Also groundbreaking are the results of a technical study of the paintings, which constitutes a major contribution to the scholarship on the Le Nain brothers.
The author, a well-known astronomer himself, describes the evolution of astronomical ideas, touching only lightly on most of the instrumental developments. Richly illustrated, the book starts with the astronomical ideas of the Egyptian and Mesopotamian philosophers, moves on to the Greek period and then on to the golden age of astronomy, that of Copernicus, Galileo, Kepler and Newton. Finally, Pecker concludes with modern theories of cosmology. Written with astronomy undergraduates in mind, this is a fascinating survey of astronomical thinking.
A comprehensive handbook of more than 1,000 magical words, phrases, symbols, and secret alphabets • Explains the origins, derivatives, and practical usage of each word, phrase, and spell as well as how they can be combined for custom spells • Based on the magical traditions of Europe, Greece, and Egypt and recently discovered one-of-a-kind grimoires from Scandinavia, France, and Germany • Includes an in-depth exploration of secret magical alphabets, including those based on Hebrew letters, Kabbalistic symbols, astrological signs, and runes From Abracadabra to the now famous spells of the Harry Potter series, magic words are no longer confined to the practices of pagans, alchemists, witches, and occultists. They have become part of the popular imagination of the Western world. Passed down from ancient Babylon, Egypt, and Greece, these words and the rituals surrounding them have survived through the millennia because they work. And as scholar Claude Lecouteux reveals, often the more impenetrable they seem, the more effective they are. Analyzing more than 7,000 spells from the magical traditions of Europe as well as the magical papyri of the Greeks and recently discovered one-of-a-kind grimoires from Scandinavia, France, and Germany, Lecouteux has compiled a comprehensive dictionary of ancient magic words, phrases, and spells along with an in-depth exploration--the first in English--of secret magical alphabets, including those based on Hebrew letters, Kabbalistic symbols, astrological signs, and runes. Drawing upon thousands of medieval accounts and famous manuscripts such as the Heptameron of Peter Abano, the author examines the origins of each word or spell, offering detailed instructions on their successful use, whether for protection, love, wealth, or healing. He charts their evolution and derivations through the centuries, showing, for example, how spells that were once intended to put out fires evolved to protect people from witchcraft. He reveals the inherent versatility of magic words and how each sorcerer or witch had a set of stock phrases they would combine to build a custom spell for the magical need at hand. Presenting a wealth of material on magical words, signs, and charms, both common and obscure, Lecouteux also explores the magical words and spells of ancient Scandinavia, the Hispano-Arabic magic of Spain before the Reconquista, the traditions passed down from ancient Egypt, and those that have stayed in use until the present day.
The conference was aimed at promoting contacts between scientists involved in solar-terrestrial physics, space physics, astroparticle physics and cosmology both from the theoretical and the experimental approach. The conference was devoted to physics and physics requirements, survey of theoretical models and performances of detectors employed (or to be employed) in experiments for fundamental physics, astroparticle physics, astrophysics research and space environment - including Earth magnetosphere and heliosphere and solar-terrestrial physics. Furthermore, cosmic rays have been used to extent the scientific research experience to teachers and students with air shower arrays and other techniques. Presentations included the following subjects: advances in physics from present and next generation ground and space experiments, dark matter, double-beta decay, high-energy astrophysics, space environment, trapped particles, propagation of cosmic rays in the Earth atmosphere, Heliosphere, Galaxy and broader impact activities in cosmic rays science. The open and flexible format of the Conference was conducive to fruitful exchanges of points of view among participants and permitted the evaluation of the progresses made and indicated future research directions. The participants were experienced researchers but also graduate students (MSc and PhD) and recent postdoctoral fellows.
An extensive study of ancient books of magic and the magical practices preserved in the few surviving grimoires • Includes spells, talisman formulations, and secret magical alphabets reproduced from the author’s private collection of grimoires, with instructions for their use • Explains the basic principles of medieval magic, including the doctrine of names and the laws of sympathy and contagion • Offers an overview of magic in the Western Mystery tradition Grimoires began simply as quick-reference “grammar books” for sorcerers, magicians, and priests before evolving into comprehensive guides to magic, complete with spell-casting rituals, magical alphabets, and instructions to create amulets and talismans. With the advent of the printing press, some grimoires were mass produced, but many of the abbreviations were misinterpreted and magical words misspelled, rendering them ineffective. The most powerful grimoires remained not only secret but also heavily encoded, making them accessible only to the highest initiates of the magical traditions. Drawing on his own private collection of grimoires and magical manuscripts as well as his privileged access to the rare book archives of major European universities, Claude Lecouteux offers an extensive study of ancient books of magic and the ways the knowledge within them was kept secret for centuries through symbols, codes, secret alphabets, and Kabbalistic words. Touching on both white and black magical practices, he explains the basic principles of medieval magic, including the doctrine of names and signatures, mastery of the power of images, and the laws of sympathy and contagion. He gives an overview of magic in the Western Mystery tradition, emphasizing both lesser-known magicians such as Trithemus and Peter of Apono and famous ones like Albertus Magnus and Hermes Trismegistus. Creating a universal grimoire, Lecouteux provides exact reproductions of secret magical alphabets, symbols, and glyphs with instructions for their use as well as an illustrated collection of annotated spells, rituals, and talismans for numerous applications including amorous magic, healing magic, and protection rites. The author also examines the folk magic that resulted when the high magic of the medieval grimoires melded with the preexisting pagan magic of ancient Europe.
This textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations. Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory. Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject.
Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: 1. It leads more quickly to the essentials of the subject, 2. An absence of signs and orientation considerations simplifies the theory, 3. Computations and advanced applications can be presented at an earlier stage, 4. Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book.
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