WorldCat Identities

Audin, Michèle

Overview
Works: 99 works in 286 publications in 3 languages and 5,752 library holdings
Genres: History  Biography  Records and correspondence  Sources 
Roles: Editor, Interviewee, Thesis advisor, Translator
Classifications: QA445, 516
Publication Timeline
Key
Publications about  Michèle Audin Publications about Michèle Audin
Publications by  Michèle Audin Publications by Michèle Audin
Most widely held works by Michèle Audin
Théorie de Morse et homologie de Floer by Michèle Audin ( )
11 editions published between 2010 and 2014 in French and English and held by 800 WorldCat member libraries worldwide
This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. The book originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students
Géométrie by Michèle Audin ( )
7 editions published between 1998 and 2006 in French and held by 769 WorldCat member libraries worldwide
Fatou, Julia, Montel the great prize of mathematical sciences of 1918, and beyond by Michèle Audin ( )
17 editions published in 2011 in English and held by 487 WorldCat member libraries worldwide
Annotation
Fatou, Julia, Montel le grand prix des sciences mathematiques de 1918, et apres - by Michèle Audin ( )
11 editions published in 2009 in French and English and held by 408 WorldCat member libraries worldwide
Le Grand Prix, le cadre -- Le Grand Prix des Sciences Mathématiques -- Les mémoires -- Suites de l'itération -- Sur Pierre Fatou -- Une polémique en 1965
Remembering Sofya Kovalevskaya by Michèle Audin ( )
12 editions published between 2011 and 2012 in English and Undetermined and held by 404 WorldCat member libraries worldwide
Sofia Kovalevskaya was a brilliant and determined young Russian woman of the 19th century who wanted to become a mathematician and who succeeded, in often difficult circumstances, in becoming arguably the first woman to have a professional university career in the way we understand it today. This memoir, written by a mathematician who specialises in symplectic geometry and integrable systems, is a personal exploration of the life, the writings and the mathematical achievements of a remarkable woman. It emphasises the originality of Kovalevskaya's work and assesses her legacy and reputation as
Geometry by Michèle Audin ( Book )
13 editions published between 2002 and 2004 in English and held by 388 WorldCat member libraries worldwide
Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michèle Audin, professor at the University of Strasbourg, has written a book allowing them to remedy this situation and, starting from linear algebra, extend their knowledge of affine, Euclidean and projective geometry, conic sections and quadrics, curves and surfaces. It includes many nice theorems like the nine-point circle, Feuerbach's theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for most of the exercises are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master's level to discover geometry and deepen their knowledge and understanding
Spinning tops : a course on integrable systems by Michèle Audin ( Book )
16 editions published between 1996 and 2004 in English and French and held by 341 WorldCat member libraries worldwide
Holomorphic curves in symplectic geometry by Michèle Audin ( Book )
12 editions published in 1994 in English and held by 292 WorldCat member libraries worldwide
This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises
The topology of torus actions on symplectic manifolds by Michèle Audin ( Book )
13 editions published between 1989 and 1991 in English and French and held by 262 WorldCat member libraries worldwide
This is an extended second edition of "The Topology of Torus Actions on Symplectic Manifolds" published in this series in 1991. The material and references have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity theorems, it contains much more results, proofs and examples. Chapter I deals with Lie group actions on manifolds. In Chapters II and III, symplectic geometry and Hamiltonian group actions are introduced, especially torus actions and action-angle variables. The core of the book is Chapter IV which is devoted to applications of Morse theory to Hamiltonian group actions, including convexity theorems. As a family of examples of symplectic manifolds, moduli spaces of flat connections are discussed in Chapter V. Then, Chapter VI centers on the Duistermaat-Heckman theorem. In Chapter VII, a topological construction of complex toric varieties is presented, and the last chapter illustrates the introduced methods for Hamiltonian circle actions on 4-manifolds
Torus actions on symplectic manifolds by Michèle Audin ( Book )
8 editions published in 2004 in English and held by 226 WorldCat member libraries worldwide
This is an extended second edition of "The Topology of Torus Actions on Symplectic Manifolds" published in this series in 1991. The material and references have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity theorems, it contains much more results, proofs and examples. Chapter I deals with Lie group actions on manifolds. In Chapters II and III, symplectic geometry and Hamiltonian group actions are introduced, especially torus actions and action-angle variables. The core of the book is Chapter IV which is devoted to applications of Morse theory to Hamiltonian group actions, including convexity theorems. As a family of examples of symplectic manifolds, moduli spaces of flat connections are discussed in Chapter V. Then, Chapter VI centers on the Duistermaat-Heckman theorem. In Chapter VII, a topological construction of complex toric varieties is presented, and the last chapter illustrates the introduced methods for Hamiltonian circle actions on 4-manifolds
Symplectic geometry of integrable Hamiltonian systems by Michèle Audin ( Book )
7 editions published in 2003 in English and held by 202 WorldCat member libraries worldwide
Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book)
Hamiltonian systems and their integrability by Michèle Audin ( Book )
8 editions published between 2008 and 2009 in English and held by 136 WorldCat member libraries worldwide
"This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates. These techniques include analytical methods coming from the Galois theory of differential equations, as well as more classical algebro-geometric methods related to Lax equations. This book would be suitable for a graduate course in Hamiltonian systems."--BOOK JACKET
Nouveaux invariants en géométrie et en topologie by Michèle Audin ( Book )
9 editions published between 2001 and 2002 in French and English and held by 134 WorldCat member libraries worldwide
Les premières étapes du machinisme by M Dubuisson ( Book )
1 edition published in 1965 in French and held by 130 WorldCat member libraries worldwide
Les systèmes hamiltoniens et leur intégrabilité by Michèle Audin ( Book )
6 editions published in 2001 in French and held by 126 WorldCat member libraries worldwide
Cobordismes d'immersions lagrangiennes et legendriennes by Michèle Audin ( Book )
10 editions published between 1986 and 1987 in French and held by 96 WorldCat member libraries worldwide
ON CALCULE LES GROUPES DE COBORDISME DEFINIS PAR V. I. ARNOLD POUR LES IMMERSIONS LAGRANGIENNES DANS LE FIBRE COTANGENT D'UNE VARIETE: ON LES DEDUIT DES GROUPES CORRESPONDANTS DANS LE FIBRE COTANGENT DE R**(N,) CEUX-CI SONT LES GROUPES DE COBORDISME DES VARIETES DONT LE FIBRE TANGENT COMPLEXIFIE EST TRIVIALISE; ON DEDUIT EN DETAIL LES INVARIANTS ALGEBRIQUES LIES A CETTE SITUATION, ET ON DONNE DES APPLICATIONS A LA THEORIE ENUMERATIVE DES SINGULARITES LAGRANGIENNES. ON UTILISE CES RESULTATS POUR CALCULER LES GROUPES DE COBORDISME POUR LES IMMERSIONS LEGENDRIENNES DANS DES VARIETES D'ELEMENTS DE CONTACT. LES METHODES METTENT EN JEU DE NOMBREUX ASPECTS DE LA THEORIE DU COBORDISME ET LES RESULTATS PERMETTENT DE MONTRER L'EXISTENCE D'IMMERSIONS LAGRANGIENNES OU LEGENDRIENNES AYANT CERTAINES PROPRIETES ALORS MEME QUE FORT PEU D'EXEMPLES EXPLICITES SONT CONNUS
Correspondance entre Henri Cartan et André Weil (1928-1991) by Henri Cartan ( Book )
5 editions published in 2011 in 3 languages and held by 74 WorldCat member libraries worldwide
Jacques Feldbau, Topologe : Das Schicksal eines jüdischen Mathematikers (1914 - 1945) by Michèle Audin ( )
6 editions published in 2012 in German and held by 69 WorldCat member libraries worldwide
Souvenirs sur Sofia Kovalevskaya by Michèle Audin ( Book )
5 editions published in 2008 in French and held by 62 WorldCat member libraries worldwide
Une histoire de Jacques Feldbau by Michèle Audin ( Book )
5 editions published between 2009 and 2010 in French and held by 46 WorldCat member libraries worldwide
 
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Alternative Names
Audin, Michele
Languages
English (109)
French (65)
German (6)
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