This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
The notebooks of Captain Coignet (1776-1865) are possibly the most legendary account of the services of a young conscript and his experiences under Napoleon’s consulate and empire. Having distinguished himself at the battle of Montebello, and awarded an arme d’honneur, he is inducted into the famed Grenadiers of the Imperial Guard (having cheated the height restriction with the connivance of the normally strict Davout and four packs of playing cards in his stockings). Despite being illiterate until late into his adult life, due to his rough childhood as recounted in the first notebook, many famous personalities of the Empire are sketched in his honest style, although his own memory has somewhat embellished the facts. Prof. Jean Tulard refers to them as indispensible for understanding the mentality of the “grognard” or grumbler, the stalwart veterans of Napoleon’s Guard. This edition benefits from a preface by Lorédan Larchey (1831-1902) author of numerous French historical works, and over a hundred illustrations. Includes 101 illustrations and TOC
Perhaps the most famous of all Napoleonic memoirs to be written in any language are those written by Marbot. They stand in a league of their own. Napoleon, himself left a donation of 100,000 to him, for his refutation of General Rogniat's work - to quote Napoleon's will "I recommend him to continue to write in defense of the glory of the French armies, and to confound their calumniators and apostates." So entertaining and full of vivid details that Sir Arthur Conan Doyle fictionalized them into his adventures of Brigadier Gerard. In this the first volume of his translated memoirs, it covers his early childhood, born into a military family, to his first steps on the military ladder as a hussar in the 1e Regiment de Hussards (ex-Bercheny). His dash and leadership lead to a commission and appointments on the staff of Generals Augereau and Masséna. He writes poignantly of his fathers death at the siege of Genoa (1800) and the privations suffered in the city by the defenders and the inhabitants alike. His career takes him to the battles of Austerlitz, Friedland, Eylau and Aspern-Essling. His narrative is full of anecdotes and vignettes of the great and the good of the Consulate and Empire, he portrays himself in the midst of such luminaries as the Emperor, his Marshals and Generals. Contains portrait of de Marbot from 1812 as a colonel of 23e Hussards, and maps illustrating the 1805, 1806 and 1809 battles. Author - Jean Baptiste Antoine Marcelin, Baron de Marbot, 1782-1854 Translator - Arthur John Butler 1844-1910
The much wounded Count Rapp recounts his services under the Emperor Napoleon across Europe and into the depths of Russia. His frequent battlefield exploits, including a decisive charge with the Imperial Guard cavalry at Austerlitz, are balanced by polished descriptions of the court of the First Empire. Rapp's rise is charted from obscurity in the armies of the Republic to catching the attention of General Desaix whilst fighting on the Rhine, and thereafter General Bonaparte in Egypt and Italy, to the pinnacle of rank as the Emperor's first aide-de-camp, Général de Division, and Count of the Empire. Author – Général de Division, Comte Jean Rapp (1771 – 1821) Annotations – PP-Publishing
As the tide of the French revolution swept away the noble privileges many of high birth fled the country, some officers stayed despite the danger of the revolutionaries, including both Napoleon and Anne-Jean-Marie-René Savary, loyal to the state and sniffing advancement. Savary enlisted as a volunteer and was posted to the Armies of the Sambre and Meuse rivers and then the Rhine, his distinguished services led him to selected as an aide-de-camp of General Desaix who was known as a shrewd judge of characters both of men and of soldiers. It was in the sands of the desert during the Egyptian Campaign in 1798 that Savary met Napoleon he would serve faithfully for the next 17 years in the almost unbroken conflict that scarred Europe. He served admirably with his old commander Desaix during the Italian Campaign in 1800, after Desaix fell at the battle of Marengo Napoleon decided to take Savary into his confidence and appointed him head of his bodyguard. Promoted to Général de Division in 1805 shortly before the Austerlitz campaign. Once again he displayed great gallantry and courage during the fighting, but Napoleon saw that his abilities were also of use away from the field, and started to use him as a diplomat upon who he could always rely. After further missions, particularly in intrigues in Spain, Savary was appointed Minister of Police in 1810, he discharged his duties with a zeal that would not have been out of place in the Spanish Inquisition but was at fault during the attempted coup d’état of General Malet in 1812 whilst the Grande Armée was struggling through the snows of Russia. He served on as a faithful servant of Napoleon until the bitter end after Waterloo in 1815, and was considered dangerous enough to be refused permission to go the Elba with his former master. The First Volume includes his early years in the army, Egypt, the Italian campaign, treasons of Moreau and Pichegru, the 1805 Austerlitz Campaign and the Jena campaign 1806.
During the Peninsular War in Spain from 1808 to 1813, Marshal Suchet not only successfully fought the Spanish “Guerillas” but he also skilfully administrated the province of Aragon. He made it a relatively safe and prosperous place for his troops, while the rest of Spain became a nightmarish quagmire for the French occupiers. In early 1808, Napoleon, under the pretext of a dispute between the Spanish King Charles IV and his son Ferdinand, invaded Spain. His troops were at first greeted as liberators by the populace, who wanted to be rid of King Charles’ Prime Minister Manuel de Godoy. As it became clearer that Napoleon’s intentions were to take control of the Spanish kingdom and to crown his own brother, Joseph, as King, the people of Spain revolted. Appointed the governor of the insurgency-troubled province of Aragon after he had seized its main cities, Marshall Suchet skilfully adopted a balanced policy mixing strong military action and economic reforms to regenerate the local economy. He also adopted political measures aimed at restoring the appearance of a Spanish sovereignty. At the operational level, Suchet restored the discipline of III Corps and developed a network of strong places that ensured a French armed presence throughout the region while relying on highly mobile autonomous units to chase the guerrillas in their strongholds. An astute economist, he succeeded in developing the local economy, while also establishing a mutual beneficial relationship between his troops and the populace. Politically and culturally aware of the Spanish situation, he utilized the specificities of the Aragonese people to thwart the influence of the guerrilla leaders. He eventually established a flexible policy based on a mix of benevolence and coercion. During his administration, Aragon remained a relatively safe place, with a sustainable economy and, above all, one where the French soldiers and the population could mix and establish contacts.
From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.
At the turn of the 20th Century, the historical section of the French General Staff began to produce some of the most valuable and detailed studies of the Napoleonic period, and particularly Napoleon’s method for success in war. This upsurge in French military writing, and particularly of the period of greatest French success, was, not coincidentally, foreshadowed the upcoming hostilities with Germany during which Colonel Vachée was to serve in the French artillery. He wrote “Napoleon en Campagne”, of which this book is the English translation, to try to codify the rules of warfare for his contemporary French officers. Using the 1806 Jena campaign (an interesting counter viewpoint to Field Marshal Von der Gotlz’s - Jena to Eylau written from the Prussian point of view of the same campaign) as an example of Napoleon’s method of victory, Vachée gives a detailed account of the Emperor’s closest collaborators: Marshal Berthier, Generals Bacler d’Albe, Bailly de Monthion, Gourgaud, Montholon, Caulaincourt, his secretaries Bourienne, Méneval and Fain et al. He illustrates the methods used to inspire his men from the highest Marshal of the Empire to the lowliest grognard, and the punishments for failure, both on and off the battlefield. An excellent book, useful for the study of command in wartime and the Napoleonic methods in particular.
This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopy-theoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic $K$-theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopy-invariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics.
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.
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
In 1795 - the year Napoleon Bonaparte was appointed commander-in-chief in Italy - the seventeen-year-old Jean-Nicolas-Auguste Noel entered the Artillery School at Chalons. A year later, with Napoleon proclaiming himself the liberator of Italy, Noel was appointed second lieutenant in the 8th Regiment of Horse Artillery. Written in 1850, With Napoleon's Guns is his remarkable memoir of twenty years in the Emperor's service. A trained artilleryman himself, Napoleon dramatically transformed the role of the artillery from a cumbersome and tactically limited force into fluid, independent and highly mobile trains d'artillerie. This new organisation required fresh new officers - officers with intelligence who could act under their own initiative: officers such as Noel. From the optimism of the early years in Italy, through the privations of the retreat from Moscow and the horrors of the Battle of Leipzig, to the disillusionment of the Emperor's decline, Noel charts both his personal career and, at close hand, the trajectory of the First Empire with frankness and percipience. Based on the journal he kept from his cadetship at Chalons, With Napoleon's Guns is a dignified and revealing account of an officer at the heart of Napoleon's army.In 1795 - the year Napoleon Bonaparte was appointed commander-in-chief in Italy - the seventeen-year-old Jean-Nicolas-Auguste Noel entered the Artillery School at Chalons. A year later, with Napoleon proclaiming himself the liberator of Italy, Noel was appointed second lieutenant in the 8th Regiment of Horse Artillery. Written in 1850, With Napoleon's Guns is his remarkable memoir of twenty years in the Emperor's service. A trained artilleryman himself, Napoleon dramatically transformed the role of the artillery from a cumbersome and tactically limited force into fluid, independent and highly mobile trains d'artillerie. This new organisation required fresh new officers - officers with intelligence who could act under their own initiative: officers such as Noel. From the optimism of the early years in Italy, through the privations of the retreat from Moscow and the horrors of the Battle of Leipzig, to the disillusionment of the Emperor's decline, Noel charts both his personal career and, at close hand, the trajectory of the First Empire with frankness and percipience. Based on the journal he kept from his cadetship at Chalons, With Napoleon's Guns is a dignified and revealing account of an officer at the heart of Napoleon's army.In 1795 - the year Napoleon Bonaparte was appointed commander-in-chief in Italy - the seventeen-year-old Jean-Nicolas-Auguste Noel entered the Artillery School at Chalons. A year later, with Napoleon proclaiming himself the liberator of Italy, Noel was appointed second lieutenant in the 8th Regiment of Horse Artillery. Written in 1850, With Napoleon's Guns is his remarkable memoir of twenty years in the Emperor's service. A trained artilleryman himself, Napoleon dramatically transformed the role of the artillery from a cumbersome and tactically limited force into fluid, independent and highly mobile trains d'artillerie. This new organisation required fresh new officers - officers with intelligence who could act under their own initiative: officers such as Noel. From the optimism of the early years in Italy, through the privations of the retreat from Moscow and the horrors of the Battle of Leipzig, to the disillusionment of the Emperor's decline, Noel charts both his personal career and, at close hand, the trajectory of the First Empire with frankness and percipience. Based on the journal he kept from his cadetship at Chalons, With Napoleon's Guns is a dignified and revealing account of an officer at the heart of Napoleon's army.
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
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