Séminaire Nicolas Bourbaki
Encyclopedia
The Séminaire Nicolas Bourbaki (Bourbaki Seminar) is a series of seminar
s (in fact public lectures with printed notes distributed) that has been held in Paris since 1948. It is one of the major institutions of contemporary mathematics, and a barometer of mathematical achievement, fashion, and reputation. It is named after Nicolas Bourbaki
, a group of French and other mathematicians of variable membership.
The Poincaré Seminars are a series of talks on physics inspired by the Bourbaki seminars on mathematics.
For later years see
Seminar
Seminar is, generally, a form of academic instruction, either at an academic institution or offered by a commercial or professional organization. It has the function of bringing together small groups for recurring meetings, focusing each time on some particular subject, in which everyone present is...
s (in fact public lectures with printed notes distributed) that has been held in Paris since 1948. It is one of the major institutions of contemporary mathematics, and a barometer of mathematical achievement, fashion, and reputation. It is named after Nicolas Bourbaki
Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym under which a group of 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality...
, a group of French and other mathematicians of variable membership.
The Poincaré Seminars are a series of talks on physics inspired by the Bourbaki seminars on mathematics.
1948/49 series
- 1 Henri CartanHenri CartanHenri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan.-Life:...
Les travaux de Koszul, I (Lie algebra cohomologyLie algebra cohomologyIn mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was defined by in order to give an algebraic construction of the cohomology of the underlying topological spaces of compact Lie groups...
) - 2 Claude Chabauty Le théorème de Minkowski-Hlawka (Minkowski-Hlawka theorem)
- 3 Claude ChevalleyClaude ChevalleyClaude Chevalley was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups...
L'hypothèse de Riemann pour les corps de fonctions algébriques de caractéristique p, I, d'après Weil (local zeta-functionLocal zeta-functionIn number theory, a local zeta-functionis a function whose logarithmic derivative is a generating functionfor the number of solutions of a set of equations defined over a finite field F, in extension fields Fk of F.-Formulation:...
) - 4 Roger GodementRoger GodementRoger Godement is a French mathematician, known for his work in functional analysis, and also his expository books.He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan...
Groupe complexe unimodulaire, I : Les représentations unitaires irréductibles du groupe complexe unimodulaire, d'après Gelfand et Neumark (representation theoryRepresentation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
of the complex special linear groupSpecial linear groupIn mathematics, the special linear group of degree n over a field F is the set of n×n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion....
) - 5 Léo Kaloujnine Sur la structure de p-groupes de Sylow des groupes symétriques finis et de quelques généralisations infinies de ces groupes (Sylow theorems, symmetric groupSymmetric groupIn mathematics, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself...
s, infinite group theory) - 6. Pierre SamuelPierre SamuelPierre Samuel was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic. Other books of his covered projective geometry and algebraic number theory...
(birational geometryBirational geometryIn mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. In the case of dimension two, the birational geometry of algebraic surfaces was largely worked out by the Italian...
) - 7 Jean Braconnier Sur les suites de composition d'un groupe et la tour des groupes d'automorphismes d'un groupe fini, d'après H. Wielandt (finite groupFinite groupIn mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of...
s) - 8 Henri Cartan, Les travaux de Koszul, II (see 1)
- 9 Claude Chevalley, L'hypothèse de Riemann pour les groupes de fonctions algébriques de caractéristique p, II,, d'après Weil (see 3)
- 10 Luc GauthierLuc GauthierLuc Gauthier is a retired Canadian professional ice hockey defenceman who played 3 games in the National Hockey League for the Montreal Canadiens.-External links:...
, (see 6) - 11 Laurent SchwartzLaurent SchwartzLaurent-Moïse Schwartz was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work...
, Sur un mémoire de Petrowsky : "Über das Cauchysche Problem für ein System linearer partieller Differentialgleichungen im gebiete nichtanalytischen Funktionen" (partial differential equationPartial differential equationIn mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s) - 12 Henri Cartan, Les travaux de Koszul, III (see 1)
- 13 Roger Godement, Groupe complexe unimodulaire, II : La transformation de Fourier dans le groupe complexe unimodulaire à deux variables, d'après Gelfand et Neumark (see 4)
- 14 Marc Krasner, Les travaux récents de R. Brauer en théorie des groupes (finite groupFinite groupIn mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of...
s) - 15 Laurent Schwartz, Sur un deuxième mémoire de Petrowsky : "Über das Cauchysche Problem für System von partiellen Differentialgleichungen" (see 11)
- 16 André WeilAndré WeilAndré Weil was an influential mathematician of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work in number theory and algebraic geometry...
Théorèmes fondamentaux de la théorie des fonctions thêta, d'après des mémoires de Poincaré et Frobenius (theta functions)
1949/50 series
- 17 André Blanchard, Groupes algébriques et équations différentielles linéaires, d'après E. Kolchin (differential Galois theoryDifferential Galois theoryIn mathematics, differential Galois theory studies the Galois groups of differential equations.Whereas algebraic Galois theory studies extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e. fields that are equipped with a derivation, D. Much of...
) - 18 Jean DieudonnéJean DieudonnéJean Alexandre Eugène Dieudonné was a French mathematician, notable for research in abstract algebra and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of...
, Géométrie des espaces algébriques homogènes, d'après W. L. Chow (algebraic geometryAlgebraic geometryAlgebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
) - 19 Roger GodementRoger GodementRoger Godement is a French mathematician, known for his work in functional analysis, and also his expository books.He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan...
, Sommes continues d'espaces de Hilbert, I (functional analysisFunctional analysisFunctional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, direct integralDirect integralIn mathematics and functional analysis a direct integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers...
s) - 20 Charles PisotCharles PisotCharles Pisot was a French mathematician. He is chiefly recognized as one of the primary investigators of the numerical set associated with his name, the Pisot–Vijayaraghavan numbers....
, Démonstration élémentaire du théorème des nombres premiers, d'après Selberg et Erdös (prime number theoremPrime number theoremIn number theory, the prime number theorem describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers....
) - 21 Georges ReebGeorges ReebGeorges Henri Reeb was a French mathematician. He worked in differential topology, differential geometry, differential equations, topological dynamical systems theory and non-standard analysis....
, Propriétés des trajectoires de certains systèmes dynamiques (dynamical systems) - 22 Pierre SamuelPierre SamuelPierre Samuel was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic. Other books of his covered projective geometry and algebraic number theory...
, Anneaux locaux ; introduction à la géométrie algébrique (local ringLocal ringIn abstract algebra, more particularly in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields examined at a particular place, or...
s) - 23 Marie-Hélène Schwartz, Compte-rendu de travaux de M. Heins sur diverses majorations de la croissance des fonctions analytiques et sous-harmoniques (complex analysisComplex analysisComplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, subharmonic functionSubharmonic functionIn mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory....
s) - 24 Charles EhresmannCharles EhresmannCharles Ehresmann was a French mathematician who worked on differential topology and category theory. He is known for work on the topology of Lie groups, the jet concept , and his seminar on category theory.He attended the École Normale Supérieure in Paris before performing one year of military...
, Les connexions infinitésimales dans un espace fibré différentiable (connectionsConnection (mathematics)In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of data one wants to transport...
on fiber bundleFiber bundleIn mathematics, and particularly topology, a fiber bundle is intuitively a space which locally "looks" like a certain product space, but globally may have a different topological structure...
s) - 25 Roger Godement, Sommes continues d'espaces de Hilbert, II (see 19)
- 26 Laurent SchwartzLaurent SchwartzLaurent-Moïse Schwartz was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work...
, Sur un mémoire de K. Kodaira : "Harmonic fields in riemannian manifolds (generalized potential theory)", I (Hodge theoryHodge theoryIn mathematics, Hodge theory, named after W. V. D. Hodge, is one aspect of the study of the algebraic topology of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised...
) - 27 Jean-Pierre SerreJean-Pierre SerreJean-Pierre Serre is a French mathematician. He has made contributions in the fields of algebraic geometry, number theory, and topology.-Early years:...
, Extensions de groupes localement compacts, d'après Iwasawa et Gleason (locally compact groupLocally compact groupIn mathematics, a locally compact group is a topological group G which is locally compact as a topological space. Locally compact groups are important because they have a natural measure called the Haar measure. This allows one to define integrals of functions on G.Many of the results of finite...
s) - 28 René ThomRené ThomRené Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
, Les géodésiques dans les variétés à courbure négative, d'après Hopf (geodesicGeodesicIn mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...
s) - 29 Armand BorelArmand BorelArmand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993...
, Groupes localement compacts, d'après Iwasawa et Gleason (see 27) - 30 Jacques DixmierJacques DixmierJacques Dixmier is a French mathematician. He worked on operator algebras, and wrote several of the standard reference books on them, and introduced the Dixmier trace. He received his Ph.D. in 1949 from the University of Paris, and his students include Alain Connes.-Publications:*J. Dixmier,...
, Facteurs : classification, dimension, trace (von Neumann algebraVon Neumann algebraIn mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann, motivated by his study of single operators, group...
s) - 31 Jean-Louis KoszulJean-Louis KoszulJean-Louis Koszul is a mathematician best known for studying geometry and discovering the Koszul complex.He was educated at the Lycée Fustel-de-Coulanges in Strasbourg before studying at the Faculty of Science in Strasbourg and the Faculty of Science in Paris...
, Algèbres de Jordan (Jordan algebraJordan algebraIn abstract algebra, a Jordan algebra is an algebra over a field whose multiplication satisfies the following axioms:# xy = yx # = x ....
s) - 32 Laurent Schwartz, Sur un mémoire de K. Kodaira : "Harmonic fields in riemannian manifolds (generalized potential theory)", II (see 26)
For later years see
- Séminaire Nicolas Bourbaki (1950–1959)
- Séminaire Nicolas Bourbaki (1960–1969)
- Séminaire Nicolas Bourbaki (1970–1979)
- Séminaire Nicolas Bourbaki (1980–1989)
- Séminaire Nicolas Bourbaki (1990–1999)
Publishers
The proceedings of the Séminaire have been published by four different publishers over the years. 1948/49 through 1964/65 were published as Textes des conférences / Séminaire Bourbaki by the Secrétariat Mathématique, Université Paris. In 1966, W. A. Benjamin, Inc. issued a special twelve-volume facsimile reproduction of the Séminaire Bourbaki, 1948-1965. W. A. Benjamin, Inc. continued to publish the proceedings for three more years, 1965/66 through 1967/68. Springer-Verlag published 1968/69 through 1980/81 as part of its Lecture Notes in Mathematics series. 1981/82 to date are published by the Société Mathématique de France as part of Astérisque.External links
- Copies of the Séminaire papers
- Source list
- "L'Association des Collaborateurs de Nicolas Bourbaki" The pdf file of seminar number (say) 984 is available at http://www.bourbaki.ens.fr/TEXTES/984.pdf.