WorldCat Identities

Gromov, Mikhael 1943-

Works: 78 works in 291 publications in 4 languages and 4,143 library holdings
Genres: Conference papers and proceedings  Exhibition catalogs  Nonfiction films  Filmed lectures  Quotations  History 
Roles: Author, Editor, Honoree, Other, Dedicatee, Thesis advisor, Creator, Opponent, Contributor
Publication Timeline
Most widely held works by Mikhael Gromov
Pattern formation in biology, vision and dynamics by Alessandra Carbone( )

12 editions published between 1999 and 2000 in English and held by 979 WorldCat member libraries worldwide

Half a billion years of evolution have turned the eye into an unbelievable pattern detector. Everything we perceive comes in delightful multicolored forms. Now, in the age of science, we want to comprehend what and why we see. Two dozen outstanding biologists, chemists, physicists, psychologists, computer scientists and mathematicians met at the Institut d'Hautes Etudes Scientifiques in Bures-sur-Yvette, France. They expounded their views on the physical, biological and physiological mechanisms creating the tapestry of patterns we see in molecules, plants, insects, seashells, and even the human
Metric structures for Riemannian and non-Riemannian spaces by Mikhael Gromov( )

44 editions published between 1998 and 2007 in English and held by 592 WorldCat member libraries worldwide

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov-Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy-Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices--by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures--as well as an extensive bibliography and index round out this unique and beautiful book
Partial differential relations by Mikhael Gromov( Book )

22 editions published between 1986 and 2010 in 3 languages and held by 523 WorldCat member libraries worldwide

The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book
Different faces of geometry by S. K Donaldson( )

14 editions published in 2004 in English and held by 402 WorldCat member libraries worldwide

Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: Amoebas and Tropical Geometry Convex Geometry and Asymptotic Geometric Analysis Differential Topology of 4-Manifolds 3-Dimensional Contact Geometry Floer Homology and Low-Dimensional Topology Khler Geometry Lagrangian and Special Lagrangian Submanifolds Refined Seiberg-Witten Invariants. These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvth (USA) and Z. Szab (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). "One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in low-dimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvth and Szab). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun. Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Khler and algebraic manifolds), a point which is also made by Bauer in the context of 4-manifolds and the "11/8 conjecture". LeBrun's article gives another perspective on 4-manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even "well-known" 4-manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the "geometry" is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra. The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebro-topological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems."--The Preface by the Editors
Manifolds of nonpositive curvature by Werner Ballmann( Book )

18 editions published in 1985 in 3 languages and held by 396 WorldCat member libraries worldwide

This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collge de France in Paris. Among others these lectures threat local and global rigidity problems (e.g., a generalization of the famous Mostow rigidity theorem) and finiteness results for manifolds of finite volume. V. Schroeder wrote up these lectures, including complete and detailed proofs. A lot of background material is added to the first lectures. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank
Metric structures for Riemannian and non-Riemannian spaces by Mikhael Gromov( Book )

2 editions published in 1999 in English and held by 267 WorldCat member libraries worldwide

Mathematics : a beautiful elsewhere by Hervé Chandès( Recording )

3 editions published between 2011 and 2012 in English and held by 178 WorldCat member libraries worldwide

Based on an exhibition with the same name, explores the aesthetic aspects of mathematics through art, and features the exhibition's soundtrack on an accompanying CD
Structures métriques pour les variétés riemanniennes by Mikhael Gromov( Book )

8 editions published in 1981 in French and held by 106 WorldCat member libraries worldwide

Geometric group theory : proceedings of the symposium held in Sussex, 1991 by Mikhael Gromov( Book )

25 editions published between 1993 and 2005 in English and held by 104 WorldCat member libraries worldwide

The articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. This second volume contains solely a ground breaking paper by Gromov, which provides a fascinating look at finitely generated groups. For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library
Great circle of mysteries : mathematics, the world, the mind by Mikhael Gromov( )

2 editions published in 2018 in English and held by 99 WorldCat member libraries worldwide

"The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these "systems" may serve as prototypes for design of universal learning computer programs."--Publisher
Geometries in interaction : GAFA special issue in honor of Mikhail Gromov by Y Eliashberg( Book )

10 editions published between 1995 and 2003 in English and held by 85 WorldCat member libraries worldwide

Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. Piatetski-Shapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics
Asymptotic theory of finite dimensional normed spaces by Vitali D Milman( Book )

9 editions published between 1986 and 2001 in English and held by 65 WorldCat member libraries worldwide

Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other. The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics)
Geometric topology : recent developments : lectures given on the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held at Montecatini Terme, Italy, June 4-12, 1990 by Jeff Cheeger( )

5 editions published in 1991 in English and Undetermined and held by 47 WorldCat member libraries worldwide

Geometric Topology can be defined to be the investigation of global properties of a further structure (e.g. differentiable, Riemannian, complex, algebraic etc.) one can impose on a topological manifold. At the C.I.M.E. session in Montecatini, in 1990, three courses of lectures were given onrecent developments in this subject which is nowadays emerging as one of themost fascinating and promising fields of contemporary mathematics. The notesof these courses are collected in this volume and can be described as: 1) the geometry and the rigidity of discrete subgroups in Lie groups especially in the case of lattices in semi-simple groups; 2) the study of the critical points of the distance function and its appication to the understanding of the topology of Riemannian manifolds; 3) the theory of moduli space of instantons as a tool for studying the geometry of low-dimensional manifolds. CONTENTS: J. Cheeger: Critical Points of Distance Functions and Applications to Geometry.- M. Gromov, P. Pansu, Rigidity of Lattices: An Introduction.- Chr. Okonek: Instanton Invariants and Algebraic Surfaces
Pattern formation in morphogenesis : problems and mathematical issues by Vincenzo Capasso( )

10 editions published between 2011 and 2013 in English and held by 46 WorldCat member libraries worldwide

Pattern Formation in Morphogenesis is a rich source of interesting and challenging mathematical problems. The volume offers an interdisciplinary interaction space between biologists working in this field and mathematicians, who may propose solutions to the problems put forward by biologists. The main goal is to facilitate the process of cultivating a mutual recognition of the complementary skills between biologists and mathematicians, to the point where the resulting synergy generates new and novel discoveries in the field of Developmental Biology. Lastly, the volume shows how a combination of new discoveries in developmental biology and associated mathematical modeling and computational techniques has stimulated or may stimulate relevant advances in the field.                             
Introduction aux mystères by Mikhael Gromov( Book )

5 editions published in 2012 in French and held by 36 WorldCat member libraries worldwide

Dans le cadre de l'exposition Mathématiques, un dépaysement soudain, présentée du 21 octobre 2011 au 18 mars 2012, la Fondation Cartier pour l'art contemporain publie Introduction aux Mystères, un livre imaginé par le mathématicien franco-russe Misha Gromov et conçu graphiquement par l'artiste Jean-Michel Alberola. À l'origine de cette publication se trouve la Bibliothèque des Mystères, l'une des oeuvres emblématiques de l'exposition Mathématiques, un dépaysement soudain, fruit d'une collaboration étroite et inédite entre Misha Gromov et le réalisateur et artiste David Lynch, avec la complicité de la musicienne Patti Smith. Cette bibliothèque pensée par Misha Gromov pour le grand public rassemble trente livres choisis par lui, présentés sous la forme d'une installation sonore et filmique créée par le réalisateur américain
Mathematical slices of molecular biology by Alessandra Carbone( Book )

6 editions published in 2001 in French and English and held by 25 WorldCat member libraries worldwide

Soft and hard symplectic geometry by Mikhael Gromov( Visual )

8 editions published between 1986 and 2008 in English and held by 24 WorldCat member libraries worldwide

A videotaped lecture by Mikhael Gromov on soft and hard symplectic geometry
Volume and bounded cohomology by Mikhael Gromov( Book )

7 editions published between 1982 and 1983 in English and held by 14 WorldCat member libraries worldwide

Great Circle of Mysteries : Mathematics, the World, the Mind by Mikhael Gromov( )

1 edition published in 2018 in English and held by 11 WorldCat member libraries worldwide

Metric structures for Riemannian and non-Riemannian spaces by Mikhael Gromov( Book )

8 editions published between 1999 and 2007 in English and held by 10 WorldCat member libraries worldwide

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WorldCat IdentitiesRelated Identities
Metric structures for Riemannian and non-Riemannian spaces
Metric structures for Riemannian and non-Riemannian spacesPartial differential relationsDifferent faces of geometryMetric structures for Riemannian and non-Riemannian spacesGeometric group theory : proceedings of the symposium held in Sussex, 1991Asymptotic theory of finite dimensional normed spacesGeometric topology : recent developments : lectures given on the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held at Montecatini Terme, Italy, June 4-12, 1990Metric structures for Riemannian and non-Riemannian spaces
Alternative Names
Gromov, M.

Gromov, M. 1943-

Gromov, M. (Mikhael), 1943-

Gromov, Michael.

Gromov, Michael 1943-

Gromov, Michail

Gromov, Michail 1943-

Gromov, Michail. [t]

Gromov, Mihail.

Gromov, Mikhael.

Gromov Mikhael 1943-....

Gromov, Mikhael G.

Gromov, Mikhail

Gromov, Mikhail 1943-

Gromov, Mikhail Leonidovich 1943-

Gromov Mikhaïl Leonidovitch 1943-....

Gromov, Misha.

Gromov Misha 1943-....

Gromow, Michail 1943-

Gromow, Michail Leonidowitsch 1943-

Michail Gromov ruský matematik

Michail Gromov Russisch wiskundige

Michaił Gromow

Michail Leonidovič Gromov ruský matematik

Michail Leonidowitsch Gromow russischer Mathematiker

Miĥail Leonidoviĉ Gromov rusa matematikisto

Mihail Leonyidovics Gromov orosz-francia matematikus

Mihails Gromovs

Mihhail Gromov Venemaa matemaatik

Mijaíl Grómov

Mijaíl Grómov matemático ruso

Mikhael Gromov

Mikhaïl Grómov matemàtic rus

Mikhail Gromov matematico russo

Mikhaïl Gromov mathématicien franco-russe

Mikhail Leonidovich Gromov Russian mathematician

Mikhail Leonidovitsj Gromov

Громов, Михаил Леонидович математик

Громов Михайло Леонідович

Михаил Леонидович Громов советский, французский и американский математик

מיכאיל גרומוב מתמטיקאי רוסי

ميخائيل ليونيدوفيش غروموف

ميخائيل ليونيدوفيش غروموف رياضياتي روسي

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English (199)

French (17)

German (1)

Italian (1)