Search Results for Cartan


  1. Cartan Henri biography
    • Henri Paul Cartan .
    • Henri Cartan is the son of Elie Cartan and Marie-Louise Bianconi.
    • Among Henri Cartan's teachers at the Ecole Normale were Gaston Julia and his father Elie Cartan.
    • His doctoral studies were supervised by Paul Montel, whose research interests were the theory of analytic functions of a complex variable, and Cartan received his Docteur es Sciences mathematiques in 1928.
    • After being awarded his doctorate, Cartan taught at the Lycee Caen from 1928 to 1929, then at the University of Lille from 1929 to 1931.
    • It had been Cartan's friend Andre Weil who had suggested that he work on analytic functions of several complex variables and Weil told him about the work of Caratheodory.
    • Cartan published Les transformations analytiques des domaines cercles les uns dans les autres in 1930 and, since this paper contained generalisations of results proved by Heinrich Behnke, he was invited by Behnke to visit Germany in May 1931 and give a series of lectures at Munster in Westphalen where Behnke taught.
    • Cartan did visit Behnke in Munster in Westfalen for a second time before the start of World War II, accepting an invitation to go there in 1937.
    • A joint paper written by Henri and his father Elie Cartan, Les transformations des domaines cercles bornes appeared in 1931.
    • Most of the time the two mathematicians worked independently, but for this paper they were able to use Elie Cartan's expertise on Lie groups to tackle questions that Henri had been interested in.
    • The year in which this joint paper appeared was the one when Cartan left his position in Lille and, starting in November 1931, he took up a post at the University of Strasbourg.
    • A very important part of Cartan's mathematical life was taken up with Bourbaki.
    • ',8)">8] Cartan explains the background to Bourbaki:- .
    • In addition to Henri Cartan the founding members of Bourbaki at that July meeting were Andre Weil, Jean Dieudonne, Szolem Mandelbrojt, Claude Chevalley, Rene de Possel, and Jean Delsarte.
    • Cartan described how the group operated [Notices Amer.
    • Cartan was teaching at the University of Strasbourg when World War II started [Notices Amer.
    • It has to be remembered that the period of the war was one of great tragedy for the Cartan family.
    • Late in 1945, when World War II had ended, Cartan returned to the University of Strasbourg and taught there for a further two years.
    • Cartan had been invited to the United States in 1942 but he decided that he had to remain in France for the sake of his family, particularly his father who by this time was an old man.
    • We explained above that Cartan was appointed professor at the Sorbonne in Paris in November 1940.
    • At the Ecole Normale Superieure he started the Seminaire Cartan at the time that Serre was one of his doctoral students.
    • It was Serre who suggested that the seminars should be written up for publication and fifteen ENS-Seminars written by Cartan were published between 1948 and 1964.
    • Cartan worked on analytic functions, the theory of sheaves, homological theory, algebraic topology and potential theory, producing significant developments in all these areas.
    • reviewing [Henri Cartan Oeuvres (3 vols.) (Berlin-New York, 1979).',2)">2]:- .
    • A central figure in this development has been Henri Cartan, whose series of papers in this field starting in the 1920's dealt with fundamental questions relating to Nevanlinna theory, generalizations of the Mittag-Leffler and Weierstrass theorems to functions of several variables, problems concerned with biholomorphic mappings and the biholomorphic equivalence problem, domains of holomorphy and holomorphic convexity, etc.
    • The major developments in the theory from 1930 to 1950 came from Cartan and his school in France, Behnke's school in Munster, and Oka in Japan.
    • The central ideas up to that time were synthesized in Cartan's Seminaires in the early 1950's, and these were very influential to the next several generations of mathematicians.
    • Cartan's accomplishments were broad and he influenced mathematics through his writing, his teaching, his seminars, and his students in a remarkable manner.
    • In the Preface of [Henri Cartan Oeuvres (3 vols.) (Berlin-New York, 1979).',2)">2] Remmert and Serre write:- .
    • The reader should be aware that these volumes do not fully reflect H Cartan's work, a large part of which is also contained in his fifteen ENS-Seminars (1948-1964) and in his book Homological algebra with S Eilenberg.
    • In particular one cannot appreciate the importance of Cartan's contributions to sheaf theory, Stein manifolds and analytic spaces without studying his 1950/51, 1951/52 and 1953/54 Seminars.
    • We should mention another aspect of Cartan's work which has been involved with politics and in particular supporting human rights.
    • Andrei Sakharov pointed out that this was a political act and Cartan began a strenuous campaign for Plyushch's release.
    • After the Congress Cartan played a major role in setting up the Comite des Mathematiciens to support Plyushch in particular, and all dissident mathematicians.
    • In January 1976 the Soviet authorities released Plyushch which was a major success for Cartan and the Comite des Mathematiciens.
    • For his outstanding work in assisting dissidents Cartan received the Pagels Award from the New York Academy of Sciences.
    • Cartan is a member of the Academie des Sciences of Paris and of other academies in Europe, the United States, and Japan.
    • A Poster of Henri Cartan .
    • Honours awarded to Henri Cartan .
    • .

  2. Cartan biography
    • Elie Joseph Cartan .
    • Elie Cartan's mother was Anne Cottaz and his father was Joseph Cartan who was a blacksmith.
    • Cartan became a student at the Ecole Normale Superieure in 1888 and obtained his doctorate in 1894.
    • In 1903 Cartan was appointed as a professor at the University of Nancy and he remained there until 1909 when he moved to Paris.
    • He married Marie-Louise Bianconi in 1903 and they had four children, one of them Henri Cartan was to produce brilliant work in mathematics.
    • By the time they received the news of Louis' murder by the Germans, Cartan was 75 years old and it was a devastating blow for him.
    • Cartan worked on continuous groups, Lie algebras, differential equations and geometry.
    • This was shown by Cartan in his thesis when he constructed each of the exceptional simple Lie algebras over the complex field.
    • Wedderburn would complete Cartan's work in this area.
    • His work is a striking synthesis of Lie theory, classical geometry, differential geometry and topology which was to be found in all Cartan's work.
    • By 1904 Cartan was writing papers on differential equations and in many ways this work is his most impressive.
    • This enabled Cartan to define what the general solution of an arbitrary differential system really is but he was not only interested in the general solution for he also studied singular solutions.
    • Klein's Erlanger Programm was seen to be inadequate as a general description of geometry by Weyl and Veblen and Cartan was to play a major role.
    • In fact this work led Cartan to the notion of a fibre bundle although he does not give an explicit definition of the concept in his work.
    • Cartan further contributed to geometry with his theory of symmetric spaces which have their origins in papers he wrote in 1926.
    • Cartan then went on to examine problems on a topic first studied by Poincare.
    • By this stage his son, Henri Cartan, was making major contributions to mathematics and Elie Cartan was able to build on theorems proved by his son.
    • Henri Cartan said [Notices Amer.
    • Cartan discovered the theory of spinors in 1913.
    • Cartan published the two volume work Lecons sur la theorie des spineurs in 1938.
    • Cartan's recognition as a first rate mathematician came to him only in his old age; before 1930 Poincare and Weyl were probably the only prominent mathematicians who correctly assessed his uncommon powers and depth.
    • For his outstanding contributions Cartan received many honours, but as Dieudonne explained in the above quote, these did not come until late in career.
    • A Poster of Elie Cartan .
    • Honours awarded to Elie Cartan .
    • Lunar featuresCrater Cartan .
    • .

  3. Libermann biography
    • Libermann greatly benefited from the reforms brought in by Eugenie Cotton, and she was taught by leading mathematicians such as Elie Cartan, Andre Lichnerowicz and Jacqueline Ferrand.
    • Eugenie Cotton was forced to retire in 1941, but Libermann, who was one of the three Jewish students supported by the scholarships, was able to spend session 1941-42 at Ecole Sevres beginning a research career advised by Elie Cartan.
    • From that time on, Libermann had great admiration for Elie Cartan and remained a close friend of the Cartan family for the rest of her life.
    • Again she received important advice from Elie Cartan who suggested to her she contact Charles Ehresmann at the University and begin studying for a doctorate in mathematics under his supervision.
    • The equivalence problem is a general problem and has been investigated by many including the Cartan.
    • For example she gave a survey of various geometric concepts and results used in analytical mechanics in her lecture Liouville forms, parallelisms and Cartan connections to the Jean Leray '99 Conference, and reviewed and summarized the theory of Cartan connections in her lecture Cartan connections and momentum maps given at the Classical and Quantum Integrability conference held in Warsaw in 2001.
    • She liked to speak of those who helped her, either personally or professionally: Cartan's family, Jacqueline Ferrand, Ehresmann, anonymous others ..

  4. Malgrange biography
    • In his second year of study he was taught by Henri Cartan who had arrived back from a visit to Chicago and Harvard in the United States.
    • Malgrange took Cartan's courses on differential geometry and Lie groups in his second year.
    • Following a suggestion by Jean Dieudonne, enthusiastically supported by Henri Cartan, Malgrange and his fellow student Andre Blanchard spent one semester of their second year of study at the Faculty of Sciences at Nancy.
    • In his fourth year of study at the Ecole Normale Superieure, Malgrange took a course on functions of several complex variables from Henri Cartan and also attended a seminar led by Jean-Pierre Serre on the same topic.
    • After Grothendieck's thesis defense, which took place in Paris, Malgrange recalled that he, Grothendieck, and Henri Cartan piled into a taxicab to go to lunch at the home of Laurent Schwartz.
    • "In the taxi Cartan explained to Grothendieck some wrong things Grothendieck had said about sheaf theory," Malgrange recalled.
    • This work was based on ideas in the theory of distributions developed by Laurent Schwartz and also used ideas on analytic functions which had been developed by Henri Cartan.

  5. Delsarte biography
    • After one year they were joined by Henri Cartan, Jean Coulomb who studied mathematical physics, Paul Dubreil, Rene de Possel and the future philosopher of mathematics Jean Cavailles.
    • Delsarte cooperated with Andre Weil and Henri Cartan, both by this time lecturers in Strasbourg, in organising a joint seminar programme between Nancy and Strasbourg.
    • In 1953 he created the Elie Cartan Institute at Nancy which, to a certain extent, was modelled on the Henri Poincare Institute in Paris.
    • Delsarte's involvement with Bourbaki, and the continual appearance of members of Bourbaki at the Institute, led to widespread belief that the Elie Cartan Institute was the Bourbaki group.
    • The Bourbaki Group is completely distinct from the Elie Cartan Institute, which deals only with the administration of the Bourbaki Group.
    • The members of the Elie Cartan Institute are not the members of the Bourbaki Group, but the intersection of these two sets is nonempty.

  6. Yano biography
    • He entered the university and, together with some fellow students who also were keen to learn about differential geometry and Riemannian geometry, he studied some of the major texts such as those by Schouten, Weyl, Eisenhart, Levi-Civita and Cartan.
    • He read widely on the topic and decided that the ideas of Elie Cartan attracted him most.
    • He therefore decided to go to Paris to study with Cartan and began to work for one of three science scholarships which were awarded for Japanese students each year to study for two years in France.
    • S S Chern had also gone to Paris at the same time to work with Cartan.
    • The author says in the preface that the chief purpose of this book is to explain E Cartan's geometrical interpretation of the concept "connection," as plainly as possible and to make clear its relations to other new differential geometries.

  7. Pontryagin biography
    • In 1934 Cartan visited Moscow and lectured in the Mechanics and Mathematics Faculty.
    • Pontryagin attended Cartan's lecture which was in French but Pontryagin did not understand French so he listened to a whispered translation by Nina Bari who sat beside him.
    • Cartan's lecture was based around the problem of calculating the homology groups of the classical compact Lie groups.
    • Cartan had some ideas how this might be achieved and he explained these in the lecture but, the following year, Pontryagin was able to solve the problem completely using a totally different approach to the one suggested by Cartan.

  8. Schwartz biography
    • While in Toulouse, he met Henri Cartan when he visited there to conduct an oral on behalf of the Ecole Normale Superieure.
    • In fact Marie-Helene also took the opportunity to talk to Henri Cartan since she wanted to resume her mathematical studies.
    • Cartan advised him to study for a doctorate at Clermont-Ferrand which is where the University of Strasbourg moved after the German armies invaded France at the start of World War II.
    • I lost no time in rushing to explain everything to Henri Cartan who ..

  9. Killing biography
    • The main tools in the classification of the semisimple Lie algebras are Cartan subalgebras and the Cartan matrix both first introduced by Killing.
    • It was Cartan, in his doctoral thesis submitted in 1894, who found concrete representations of all the exceptional simple Lie algebras (although he did not work out all the details in his thesis).
    • In many ways Cartan was so successful in presenting Killing's classification of the semisimple Lie algebras in rigorous and complete single work, that Killing has not received as much acclaim for his remarkable achievements as one might have expected.

  10. Behnke biography
    • Henri Cartan spoke of his friendship with Behnke who soon built up a vigorous research group in Munster:- .
    • Henri Cartan said:- .
    • When Henri Cartan visited Munster in 1931 there were about 200 students in the elementary mathematics classes.

  11. Vranceanu biography
    • In Paris he worked with Elie Cartan and then he went to the United States where he studied at Harvard University and Princeton University.
    • In 1928 at the International Congress of Mathematics in Bologna, the notion of a non-holonomic space which he had discovered was studied by Schouten and Cartan.
    • Vranceanu served as a member of the International Committee of the International Mathematical Union for many years and, in that capacity, he was involved in publishing the complete works of Elie Cartan.

  12. Meyer Paul-Andre biography
    • It was Raphael Salem who lent me the first edition of the treatise on integration by Stanislaw Saks, Henri Cartan who advised me to read the 'Fonctions de Variables Reelles' by Bourbaki, and Laurent Schwartz who recommended me his book on distributions.
    • He entered the Ecole Normale Superieure in 1954 still unsure whether to study physics or mathematics but after encountering rather poor physics teaching contrasted with outstanding lectures in mathematics by Henri Cartan he quickly decided to concentrate on mathematics.
    • However, as soon as he began research under Jacques Deny (1916-), who had been a student of Henri Cartan, he showed himself to be an outstanding student.

  13. Schouten biography
    • He interacted with Elie Cartan, Ludwig Berwald, Oswald Veblen, Alexander Friedmann, Arthur Eddington and Wolfgang Pauli writing joint papers with some of them.
    • For example in 1924 he published Uber die Geometrie der halb-symmetrischen Ubertragungen jointly with Alexander Friedmann, and in 1926 he published two papers written jointly with Elie Cartan: On Riemaniann geometries admitting an absolute parallelism, and On the Geometry of the Group-manifold of Simple and Semi-simple Groups.
    • It embraces both the older theories of Jacobi and Mayer and the newer theories of Cartan, Kahler and the authors.

  14. Pisot biography
    • Elie Cartan was head of the jury with Paul Montel and Arnaud Denjoy as examiners.
    • I also express sincere thanks to Elie Cartan who has kindly presented the principal results to the Academy of Sciences (4 papers, 2 in 1936 and 2 in 1937), and to Paul Montel who kindly joined Elie Cartan and Arnaud Denjoy to make up the jury.

  15. Bloch biography
    • He did subscribe to the Bulletin des Sciences Mathematiques and corresponded with a number of mathematicians such as Jacques Hadamard, Gosta Mittag-Leffler, George Polya and Henri Cartan.
    • The reference to Hypatia seems puzzling, but Henri Cartan and Jacqueline Ferrand found the following quote by Charles Kingsley (in a book published in 1853 which Bloch may well have read), describing Hypatia's reaction to seeing gladiators massacre prisoners [The Mathematical Intelligencer 10 (1) (1988), 23-26.',4)">4]:- .
    • Elie Cartan wrote the Preface to the book:- .

  16. Matsushima biography
    • He then embarked on research which enabled him to prove that Cartan subalgebras of a Lie algebra are conjugate, but due to being out of touch with current research, he was to publish this result while unaware that Chevalley had already published a proof.
    • at the invitation of Chevalley and Henri Cartan.
    • Matsushima presented some of his results to Ehresmann's seminar in Strasbourg, extending Cartan's classification of complex irreducible Lie algebras to the case of real Lie algebras.

  17. Lichnerowicz biography
    • There he studied mathematics for three years and was strongly influenced by one of his teachers, the famous Elie Cartan.
    • The approach is that of Elie Cartan, whose method of the "repere mobile," satisfying in its naturalness, is applicable to more general types of geometry.
    • Apart from its intrinsic merits, not the least of which is its simple and clear style, the book therefore provides a good introduction to the works of Cartan ..

  18. Thom biography
    • However, mathematically it was an exciting time for Thom who was to be strongly influenced by Henri Cartan and the Bourbaki approach to mathematics.
    • In 1946 Thom graduated from the Ecole Normale Superieure and then moved to Strasbourg, taking a CNRS research post, so that he could continue to work with Henri Cartan.
    • His doctorate, supervised by Henri Cartan, was awarded in 1951 for a thesis entitled Fibre spaces in spheres and Steenrod squares.

  19. Griffiths biography
    • Perhaps most important of all was Weyl's Die Idee der Riemannschen Flache but also highly significant were the papers of Elie Cartan, Hirzebruch's book Neue topologische Methoden in der algebraischen Geometrie, notes on complex manifolds by S-S Chern, and Andre Weil's Introduction a l'etude des varietes Kahleriennes.
    • This sort of observation leads directly into the use of the exterior differential systems of Elie Cartan to try to find the "geometric core", e.g., of the moduli space of Hodge structures, which led to a great deal of the author's work in the early 1980s, and which spun off into the examination of PDE invariants via the exterior differential systems in the 1990s.

  20. Davies biography
    • In Paris he spent time at the Sorbonne and at the College de France where he was greatly influenced by Elie Cartan.
    • He extended the ideas in these papers to generalisations of Riemannian manifolds such as Finsler manifolds and Cartan manifolds in later papers, for example: Lie derivation in generalized metric spaces (1939), Subspaces of a Finsler space (1945), Motions in a metric space based on the notion of area (1945), and The theory of surfaces in a geometry based on the notion of area (1947).

  21. Valiron biography
    • He happened to meet Henri Cartan when he visited Toulouse to conduct an oral on behalf of the Ecole Normale Superieure and Henri Cartan advised him to study for a doctorate at Clermont-Ferrand which is where the University of Strasbourg moved when the German armies invaded France at the start of World War II.

  22. Tits biography
    • Cartan refined this classification in 1894, correcting some errors in the proofs, and it is now known as the Killing-Cartan classification.

  23. Dowker biography
    • In 1956 Dowker published Lectures on sheaf theory which followed the approach which had been adopted by Henri Cartan.
    • Unlike the Cartan seminars, however, the exposition does not aim at conciseness.

  24. Weyl biography
    • He was not the only mathematician developing this theory, however, for Cartan also produced work on this topic of outstanding importance.
    • There I attended his lectures on the Elie Cartan calculus of differential forms and their application to electromagnetism - eloquent, simple, full of insights.

  25. Reeb biography
    • Reeb gave a talk at the conference on Finsler and Cartan spaces.
    • He explained the geometric approach to the theory of differential equations which he had adopted and indicated that it followed the approach begun by Henri Poincare, Paul Painleve and Elie Cartan.

  26. Hunt biography
    • For example A theorem of Elie Cartan (1956) in which Hunt states:- .
    • Andre Weil and Hopf and Samelson have given a topological proof of the following theorem of Elie Cartan.

  27. Rodrigues biography
    • Elie Cartan thought that Olinde Rodrigues was two separate people, one called Olinde and one called Rodrigues.
    • Several later authors, such as Temple, repeated Cartan's error.

  28. Boruvka biography
    • An obvious choice, suggested Čech, was Paris where Boruvka could work with Elie Cartan.
    • Under the influence of Eduard Čech and Elie Cartan he worked on differential geometry, then he became interested in algebra, and undertook research on groups and groupoids (algebraic systems in which the associative law does not hold).

  29. Eilenberg biography
    • Another collaboration of major importance was between Eilenberg and Henri Cartan.
    • Henri Cartan writes in [Notices Amer.

  30. Mandelbrojt biography
    • He continued working on this topic in collaboration with Henri Cartan.
    • The present lectures give an excellent account of the modern theory of classes of infinitely differentiable functions of a real variable and may be regarded as a second edition of the author's book "Series de Fourier et classes quasi-analytiques de fonctions" to include the work of the author and of Henri Cartan since that date.

  31. Kahler biography
    • He had just published his booklet entitled Einfuhrung in die Theorie der Systeme von Differentialgleichungen, which gives a treatment of the theory developed by Elie Cartan.
    • [For my thesis I] received much advice from Kahler, from whom I learned the subject of exterior differential calculus and what is now known as the Cartan-Kahler theory.

  32. Wu Wen-Tsun biography
    • Following the award of his doctorate, Wu went to Paris where he studied with Henri Cartan.
    • Thom, a student of Cartan's, had held a CNRS research post at Strasbourg while Wu was studying there and they had got to know each other at this time and exchanged mathematical ideas, beginning a good collaboration.

  33. Berwald biography
    • Berwald and E Cartan developed a general theory of two-dimensional Finsler spaces.
    • Berwald wrote a series of major papers On Finsler and Cartan geometries.

  34. Chern biography
    • At this stage Chern was forced to choose between two attractive options, namely to stay in Hamburg and work on algebra under Artin or to go to Paris and study under Cartan.
    • His time in Paris was a very productive one and he learnt to approach mathematics, as Cartan did, see [Mathematical People: Profiles and Interviews (Boston, 1985), 33-40.',2)">2]:- .

  35. Atiyah biography
    • An address concerning Atiyah's contributions was given at the Congress by Henri Cartan, see [Proceedings of the International Congress of Mathematicians, Moscow, 1966 (Moscow, 1968).',5)">5].

  36. Kostrikin biography
    • In the 1960's, Kostrikin studied infinite-dimensional Lie algebras of Cartan type for finite characteristic and, with Shafarevich, formulated a conjecture describing all simple Lie p-algebras for characteristic p > 5.

  37. Samelson biography
    • Their subject, the basic facts about structure and representations of semisimple Lie algebras, due mainly to S Lie, W Killing, E Cartan, and H Weyl, is quite classical.

  38. Oka biography
    • Henri Cartan describes in [Kiyoshi Oka : Collected papers (Berlin-Heidelberg- New York, 1984).',1)">1] the way that Oka came into the subject:- .

  39. Gromov biography
    • the Prix Elie Cartan of the Academie des Sciences of Paris (1984); the Prix de l'Union des Assurances de Paris (1989); and the Wolf Prize in Mathematics (1993).

  40. Postnikov biography
    • The author's aim is to develop the Lie theory from the very beginning up to E Cartan's theorem about the equivalence of the category of simply connected Lie groups with the category of Lie algebras.

  41. Grassmann biography
    • Grassmann's mathematical methods were slow to be adopted but eventually they inspired the work of Elie Cartan and have since been used in studying differential forms and their application to analysis and geometry.

  42. Haar biography
    • Haar and Riesz were the editors and the reputation of the journal was quickly established with mathematicians of the quality of John von Neumann, Norbert Wiener, George D Birkhoff, Henri Cartan, Antoni Zygmund, George Polya, Paul Erdős (still a student at the time) publishing a paper in the first volume.

  43. Shimura biography
    • Henri Cartan arranged a position of 'charge de recherches' for him at the Centre National de la Recherche Scientifique (National Centre for Scientific Research) in Paris.

  44. Bilimovic biography
    • Applications of integral invariants were made by Henri Poincare, Elie Cartan and George Birkhoff for the first time, and the relationships between the theory of integral invariants and Pfaff's expression underlines the importance.

  45. Ikeda biography
    • In May 1968 Arf and Langlands visited Ege University to deliver talks on The Cartan-Dieudonne Theorem and Automorphic Forms.

  46. Chevalley biography
    • spinors were a well-established tool in theoretical physics, and Elie Cartan had already published his account of the theory.

  47. Iyanaga biography
    • He also met Henri Cartan, Dieudonne and Andre Weil, and he finally returned to Tokyo in 1934.

  48. Kantorovich biography
    • The Kharkov Congress took place from 24 to 30 June 1930 and had around 500 participants although only 14 came from outside the Soviet world including Jacques Hadamard, Wilhelm Blaschke, Otto Blumenthal, Arnaud Denjoy, Szolem Mandelbrojt, Elie Cartan, and Paul Montel.

  49. Dieudonne biography
    • After completing his school studies he entered the Ecole Normale Superieure in Paris where he was inspired by Emile Picard, Jacques Hadamard, Elie Cartan, Paul Montel, Arnaud Denjoy and Gaston Julia.

  50. Segre Beniamino biography
    • After studying in Paris with Elie Cartan for the year 1926-27, supported by a Rockefeller scholarship, Segre became Francesco Severi's assistant in Rome.

  51. Heegaard biography
    • He felt it a good omen that this hope may be fulfilled by the fact that Professor Cartan was present to give the historical lecture (interspersed with personal reminiscences) entitled: "The role of Sophus Lie's theory of groups in the development of modern geometry".

  52. Sasaki biography
    • In addition Sasaki, who was by now becoming fascinated by differential geometry, read some classic differential geometry texts including ones by Blaschke, Eisenhart, Schouten, and Cartan.

  53. Choquet-Bruhat biography
    • This is an extremely elegant account of the methods of differential geometry and exterior differential systems, which as Andre Lichnerowicz says in his preface, remains faithful to the spirit of Elie Cartan.

  54. Vagner biography
    • Among Vagner's early papers we mention Differential geometry of non-linear non-holonomic manifolds in the three-dimensional Euclidean space (1940), The geometry of an (n-1)-dimensional non-holonomic manifold in an n-dimensional space (Russian) (1941), Geometric interpretation of the motion of non-holonomic dynamical systems (Russian) (1941), On the problem of determining the invariant characteristics of Liouville surfaces (Russian) (1941), and On the Cartan group of holonomicity for surfaces (1942).

  55. Molin biography
    • In his doctoral thesis On higher complex numbers which was examined in 1892, Molien classified the complex semisimple algebras; later Cartan classified the real semisimple algebras and Wedderburn in 1907 gave the result for semisimple algebras over an arbitrary field.

  56. Finsler biography
    • In fact in 1934 Cartan wrote a book Les espaces de Finsler which established Finsler's name in differential geometry.

  57. Darboux biography
    • he followed in the spirit of Gaspard Monge, and Darboux's spirit can be detected in the work of Elie Cartan.

  58. Eisenhart biography
    • The study of continuous groups of transformations inaugurated by Lie resulted in the developments by Engel, Killing, Scheffers, Schur, Cartan, Bianchi and Fubini, a chapter which closed about the turn of the century.

  59. Borel Armand biography
    • This was extremely important for him for he was able to get to know, and to learn from, Henri Cartan, Jean Dieudonne, and Laurent Schwartz.

  60. Vessiot biography
    • He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations.

  61. Cartier biography
    • Cartier entered the Ecole Normale Superieure in 1950 where Henri Cartan was his professor of mathematics and he also attended courses by Laurent Schwartz.

  62. Loday biography
    • Karoubi was one of Henri Cartan's students, having been awarded his doctorate in 1967 for his thesis Algebres de Clifford et K-theorie, and he went on to become the founder of the First European Mathematical Congress.

  63. Cosserat biography
    • among their contemporaries, only Henri Poincare (electron theory), Emile Picard (surprisingly) and Elie Cartan appreciated the work done by the brothers.

  64. Bremermann biography
    • Henri Cartan visited Munster in 1949 for the first time after the war, sharing a wealth of ideas from the French school.

  65. Bourgain biography
    • The French Academy of Sciences awarded Bourgain its Langevin Prize in 1985 and its highest award, the E Cartan Prize in 1990.

  66. Kodaira biography
    • The 1950s saw a great flowering of complex algebraic geometry, in which the new methods of sheaf theory, originating in France in the hands of Leray, Cartan and Serre, provided a whole new machinery with which to tackle global problems.

  67. Calugareanu biography
    • These included Emile Picard, Jacques Hadamard, Elie Cartan, Paul Montel, Arnaud Denjoy and Gaston Julia.

  68. Sullivan biography
    • In addition to the 1971 Oswald Veblen Prize in Geometry mentioned above, he received the 1981 Prix Elie Cartan from the French Academy of Sciences, the 1994 King Faisal International Prize for Science (mathematics), and the Ordem Scientifico Nacional by the Brazilian Academy of Sciences in 1998.

  69. Pfaff biography
    • constituted the starting point of a basic theory of integration of partial differential equations which, through the work of Jacobi, Lie, and others, has developed into a modern Cartan calculus of extreme differential forms.

  70. Stiefel biography
    • Following earlier work of H Cartan and H Weyl, he introduced the so-called Stiefel Diagram for continuous groups, relating closed semi-simple groups and discontinuous reflection groups.

  71. Grothendieck biography
    • He became one of the Bourbaki group of mathematicians which included Weil, Henri Cartan and Dieudonne.

  72. Bruhat biography
    • Bruhat published two papers which resulted from a collaboration with Henri Cartan in 1957.

  73. Cosserat Francois biography
    • among their contemporaries, only Henri Poincare (electron theory), Emile Picard (surprisingly) and Elie Cartan appreciated the work done by the brothers.

  74. Piatetski-Shapiro biography
    • Among his main achievements are: the solution of Salem's problem about the uniqueness of the expansion of a function into a trigonometric series; the example of a non symmetric homogeneous domain in dimension 4 answering Cartan's question, and the complete classification (with E Vinberg and G Gindikin) of all bounded homogeneous domains; the solution of Torelli's problem for K3 surfaces (with I Shafarevich); a solution of a special case of Selberg's conjecture on unipotent elements, which paved the way for important advances in the theory of discrete groups, and many important results in the theory of automorphic functions, e.g., the extension of the theory to the general context of semi-simple Lie groups (with I Gelfand), the general theory of arithmetic groups operating on bounded symmetric domains, the first 'converse theorem' for GL(3), the construction of L-functions for automorphic representations for all the classical groups (with S Rallis) and the proof of the existence of non arithmetic lattices in hyperbolic spaces of arbitrary large dimension (with M Gromov).

  75. Hesse biography
    • Wilhelm Meyer gave a general form of Hesse's principle of transfer in 1883 which in turn was used by Cartan in 1913 to construct all irreducible representations of a complex semisimple Lie algebra.

  76. Moisil biography
    • Moisil then went to Paris to study for the year 1930-31 where he worked with a number of mathematicians including Elie Cartan and Jacques Hadamard.

  77. Euclid biography
    • Henri Cartan, Andre Weil, Jean Dieudonne, Claude Chevalley and Alexander Grothendieck wrote collectively under the name of Bourbaki and Bourbaki's Elements de mathematiques contains more than 30 volumes.

  78. Hopf biography
    • This was to attack questions posed to him by Elie Cartan.

  79. Apery biography
    • This was largely due to the efforts of Elie Cartan who had been in contact with the German authorities making a case for his repatriation.

  80. Lie biography
    • He did this quite independently of Lie (and not it would appear in a manner which Lie found satisfactory), and it was Cartan who completed the classification of semisimple Lie algebras in 1900.

  81. Dickson biography
    • He worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan.

  82. Dynkin biography
    • Dynkin's most famous contribution to the theory of Lie algebras was his use of the "Coxeter-Dynkin diagrams" to describe and classify the Cartan matrices of semisimple Lie algebras.

  83. Dubreil-Jacotin biography
    • Marie-Louise's father put her name down for a place at the newly opened Jules-Ferry Lycee and there her brilliance was noticed by her teachers, especially the mathematics teacher who was the sister of Elie Cartan.

  84. De Rham biography
    • The original theorem of de Rham was most probably believed to be true by Poincare and was certainly conjectured (and even used!) in 1928 by E Cartan.

  85. Browder Felix biography
    • organised innumerable special sessions at regional and national meetings and was a principal organizer of the meetings that celebrated the heritage of Hilbert, E Cartan, Poincare, and Weyl.

History Topics

  1. Bourbaki 1
    • They are Henri Cartan, who is 29 years old and has been teaching at Strasbourg since 1931, and Andre Weil who was appointed in 1933 and is 27.
    • The year is 1934 and for weeks Cartan has been asking Weil how he would teach different aspects of the differential and integral calculus.
    • Weil, like Cartan, is unhappy with the recommended text, Goursat's Traite d'Analyse, and has been suggesting to him better ways to introduce various concepts in the calculus.
    • Henri Cartan and Andre Weil are regularly in Paris.
    • The mathematicians Henri Cartan, Claude Chevalley, Jean Delsarte, Jean Dieudonne, Rene de Possel and Andre Weil who meet at Cafe Capoulade are well aware of the basic problem facing French mathematics.
    • Henri Cartan [Math.
    • Henri Cartan fully understood the dangers of their approach [Math.
    • World War II, however, was having a major impact on the project with members of Bourbaki such as Andre Weil and Claude Chevalley being in the United States and only Henri Cartan and Jean Dieudonne active in continuing the development.

  2. Bourbaki 2 references
    • H Cartan, Nicolas Bourbaki und die heutige Mathematik (Westdeutscher Verlag, Cologne and Opladen, 1959).
    • H Cartan, Nicolas Bourbaki and contemporary mathematics, Math.

  3. Bourbaki 1 references
    • H Cartan, Nicolas Bourbaki und die heutige Mathematik (Westdeutscher Verlag, Cologne and Opladen, 1959).
    • H Cartan, Nicolas Bourbaki and contemporary mathematics, Math.

  4. Bourbaki 1 references
    • H Cartan, Nicolas Bourbaki und die heutige Mathematik (Westdeutscher Verlag, Cologne and Opladen, 1959).
    • H Cartan, Nicolas Bourbaki and contemporary mathematics, Math.

  5. Bourbaki 2 references
    • H Cartan, Nicolas Bourbaki und die heutige Mathematik (Westdeutscher Verlag, Cologne and Opladen, 1959).
    • H Cartan, Nicolas Bourbaki and contemporary mathematics, Math.

  6. Bourbaki 2
    • In 1958 Henri Cartan explained why Bourbaki was not growing old [Math.

  7. Quantum mechanics history
    • However the mathematics of this had been anticipated by Eli Cartan who introduced a 'spinor' as part of a much more general investigation in 1913.
      Go directly to this paragraph

Famous Curves

No matches from this section

Societies etc

  1. International Congress Speaker
    • Elie Cartan, La theorie des groupes et les recherches recentes de geometrie differentielle.
    • Elie Cartan, Sur les espaces riemanniens symetriques.
    • Elie Cartan, Quelques apergus sur le role de la theorie des groupes de Sophus Lie dans le developpement de la geometrie moderne.
    • Henri Cartan, Problemes globaux dans la theorie des fonctions analytiques de plusieurs variables complexes.
    • Henri Cartan, Sur les fonctions de plusieurs variables complexes: les espaces analytiques.

  2. French Mathematical Society
    • 1915 E Cartan .
    • 1950 Henri Cartan .

  3. Fellow of the Royal Society
    • Elie J Cartan 1947 .
    • Henri Cartan 1971 .

  4. LMS Honorary Member
    • 1939 E Cartan .
    • 1959 H Cartan .

  5. DVR Honorary Members
    • 1994 Henri Cartan .

  6. Wolf Prize
    • 1980 - Henri Cartan .

  7. Lunar features
    • (W) nnnnn Cartan .

  8. Minutes for 1955
    • A vote of thanks was passed to the visiting lecturers, Professor Reidemeister and Professor Cartan.

  9. BMC Plenary speakers
    • Cartan, H : 1955 .

  10. BMC speakers
    • Cartan, H : 1955 .

  11. BMC 1955
    • Cartan, HOn the Eilenberg-Mac Lane groups .

  12. Lunar features
    • Cartan .

  13. European Mathematical Society Prize
    • The question of the existence of Riemannian metrics with special holomony has a long history beginning with the work of Cartan.


  1. References for Cartan
    • References for Elie Cartan .
    • .
    • M A Akivis and B Rosenfeld, Elie Cartan (1869-1951) (Providence R.I., 1993).
    • R Debever (ed.), Elie Cartan-Albert Einstein : letters on absolute parallelism, 1929-1932 (Princeton, 1979).
    • J H C Whitehead, Elie Cartan, Obituary Notices of Fellows of the Royal Society of London 8 (1952).
    • J Dieudonne, Les travaux de Elie Cartan sur les groupes et algebres de Lie, Elie Cartan, 1869-1951 (hommage de l'Acad.
    • A Finzi, Obituary: Elie Cartan (Hebrew), Riveon Lematematika 8 (1954), 76-80.
    • W V D Hodge, Obituary: Elie Cartan, J.
    • A Jackson, Interview with Henri Cartan [b.
    • .
    • M Javillier, Notice necrologique sur Elie Cartan (1869-1951), C.
    • A Lichnerowicz, Elie Cartan, Elie Cartan, 1869-1951 (hommage de l'Acad.
    • S-S Chern and C Chevalley, Obituary: Elie Cartan and his mathematical work, Bull.
    • N Saltykow, La vie et l'oeuvre de Elie Cartan (Serbo-Croat), Bull.
    • .

  2. References for Cartan Henri
    • References for Henri Cartan .
    • .
    • R Remmert and J-P Serre (eds.), Henri Cartan Oeuvres (3 vols.) (Berlin-New York, 1979).
    • H Cartan, Breve analyse des travaux de Henri Cartan, in Colloque 'Analyse et Topologie' en l'Honneur de Henri Cartan, Asterisque 32-33, Soc.
    • S Dimiev and R Lazov, Henri Cartan : on the occasion of his 80th birthday (Bulgarian), Fiz.-Mat.
    • J C Griffith, Eulogy : Henri Cartan, Bull.
    • Henri Cartan, in Colloque 'Analyse et Topologie' en l'Honneur de Henri Cartan, Asterisque 32-33, Soc.
    • A Jackson, Un entretien avec Henri Cartan, Gaz.
    • A Jackson, Interview with Henri Cartan [b.
    • .
    • Liste des travaux de Henri Cartan, in Colloque 'Analyse et Topologie' en l'Honneur de Henri Cartan, Asterisque 32-33, Soc.
    • .

  3. References for Bloch
    • H Cartan and J Ferrand, The Case of Andre Bloch, The Mathematical Intelligencer 10 (1) (1988), 23-26.
    • H Cartan and J Ferrand, Le cas Andre Bloch, Cahiers du seminaire d'histoire des mathematiques 9 (Paris, 1988), 210-219.

  4. References for Einstein
    • M Biezunski, Inside the coconut : the Einstein-Cartan discussion on distant parallelism, in Einstein and the history of general relativity (Boston, MA, 1989), 315-324.
    • R Debever, Publication de la correspondance Cartan-Einstein, Acad.

  5. References for Bourbaki
    • H Cartan, Nicolas Bourbaki und die heutige Mathematik (Westdeutscher Verlag, Cologne and Opladen, 1959).
    • H Cartan, Nicolas Bourbaki and contemporary mathematics, Math.

  6. References for De Rham
    • H Cartan, Les travaux de Georges de Rham sur les varietes differentiables, in A Haefliger and R Narasimhan (eds.), Essays on Topology and Related Topics : Memoires dedies a Georges de Rham (Berlin - Heidelberg - New York, 1970).
    • H Cartan, La vie et l'oeuvre de Georges de Rham, C.

  7. References for Levi-Civita
    • E Cartan, Notice sur M Tullio Levi-Civita, C.

  8. References for Dieudonne
    • H Cartan, Jean Dieudonne (1906-1992), Gaz.

  9. References for Schwartz
    • H Cartan, Quelques souvenirs d'une longue amitie.

  10. References for Vessiot
    • E Cartan, L'oeuvre scientifique de M Ernest Vessiot, Bulletin de la Societe mathematique de France 75 (1947), 1-8.

  11. References for Eilenberg
    • H Bass, H Cartan, P Freyd, A Heller, and S Mac Lane, Samuel Eilenberg (1913-1998), Notices Amer.

  12. References for Atiyah
    • H Cartan, L'oeuvre de Michael F Atiyah, Proceedings of the International Congress of Mathematicians, Moscow, 1966 (Moscow, 1968).

  13. References for Norlund
    • H Cartan, Niels Erik Norlund (French), C.

  14. References for Nevanlinna
    • H Cartan, Notice necrologique sur Rolf Nevanlinna, Comptes rendus de l'Academie des Sciences Paris Vie Academique 291 (5-8) (1980), 56-57.

  15. References for Hopf
    • H Cartan, Heinz Hopf (1894-1971), International Mathematical Union (1972), 1-7.

  16. References for Polya
    • H Cartan, La vie et l'oeuvre de George Polya, C.

  17. References for Artin
    • H Cartan, Emil Artin, Abh.

  18. References for Denjoy
    • H Cartan, Notice necrologique sur Arnaud Denjoy, membre de la section de geometrie, Comptes rendus de l'Academie des Sciences Paris Vie Academique 279 (1974), 49-53.

Additional material

  1. L E Dickson: 'Linear algebras
    • In presenting in Parts II and IV the main theorems of the general theory, it was necessary to choose between the expositions by Molien, Cartan and Wedderburn (that by Frobenius being based upon bilinear forms and hence outside our plan of treatment).
    • In order that our treatment of the general theory shall be elementary and concrete and shall use but a very few concepts easily kept in mind, we have confined our exposition (in Part II) to the classical case of algebras whose numbers have ordinary complex coordinates and given a careful revision of the theory as presented in Cartan's fundamental paper.

  2. R L Wilder: 'Cultural Basis of Mathematics I
    • Wednesday 30 August: A Beurling, H Hopf, Henri Cartan, R L Wilder.

  3. Marie-Louise Dubreil-Jacotin
    • The sister of Elie Cartan, who taught there noticed her aptitude for mathematics.

  4. O Veblen's Opening Address to ICM 1950
    • Wednesday 30 August: A Beurling, H Hopf, Henri Cartan, R L Wilder.

  5. Veblen's Opening Address to ICM 1950
    • Wednesday 30 August: A Beurling, H Hopf, Henri Cartan, R L Wilder.

  6. Whittaker EMS Obituary.html
    • For instance, when Einstein first produced a unified field theory the lectures dealt with that theory while a course on spinors followed the publication by Cartan of his important book on the subject.

  7. Wolf Prize.html
    • 1980 - Henri Cartan and Andrei N Kolmogorov .

  8. André Weil: Rouen prison
    • As for my work, it is going so well that today I am sending Papa Cartan a note for the Comptes-Rendus.

  9. The Edinburgh Mathematical Society: the first hundred years (1883-1983) Part 2
    • For instance, when Einstein first produced a unified field theory the lectures dealt with that theory while a course on spinors followed the publication by Cartan of his important book on the subject.

  10. Jacobson: 'Theory of Rings
    • The most important names connected with this phase of the development of the theory are those of Molien, Dedekind, Frobenius and Cartan.

  11. Gruenberg: 'Relation Modules
    • This is given completely modulo only the non-singularity of the Cartan matrix.

  12. Zariski and Samuel: 'Commutative Algebra
    • The reader who wants to see how truly homological methods may be applied to commutative algebra is referred to the original papers of M Auslander, D Buchsbaum, A Grothendieck, D Rees, J-P Serre, etc., to a forthcoming book of D C Northcott, as well, of course, as to the basic treatise of Cartan-Eilenberg.


  1. Quotations by Adams Frank
    • I do feel impelled to try and say what needs to be said about a whole way of writing books on algebra from Van der Waerden to Cartan and Eilenberg.
    • Cartan doesn't lecture this way, Eilenberg doesn't lecture this way, Bass doesn't lecture this way and they don't always write this way.


  1. Mathematical Chronology
    • Cartan, in his doctoral dissertation, classifies all finite dimensional simple Lie algebras over the complex numbers.
    • Cartan and Eilenberg develop homological algebra which allows powerful algebraic methods and topological methods to be related.

  2. Chronology for 1890 to 1900
    • Cartan, in his doctoral dissertation, classifies all finite dimensional simple Lie algebras over the complex numbers.

  3. Chronology for 1950 to 1960
    • Cartan and Eilenberg develop homological algebra which allows powerful algebraic methods and topological methods to be related.

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JOC/BS August 2001