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Marcel Berger
Marcel Berger (14 April 1927 – 15 October 2016) was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France. Formerly residing in Le Castera in Lasseube, Berger was instrumental in Mikhail Gromov's accepting positions both at the University of Paris and at the IHÉS. Awards and honors *1956 Prix Peccot, Collège de France *1962 Prix Maurice Audin *1969 Prix Carrière, Académie des Sciences *1978 Prix Leconte, Académie des Sciences *1979 Prix Gaston Julia *1979–1980 President of the French Mathematical Society. *1991 Lester R. Ford Award Selected publications * Berger, M.Geometry revealed Springer, 2010. * Berger, M.: What is... a Systole? Notices of the AMS 55 (2008), no. 3, 374–376online text* * * *Berger, Marcel; Gauduchon, Paul; Mazet, Edmond: Le spectre d'une variété riemannienne. (French) Lecture Notes in Mathematics, Vol. 194 Springer-Verlag, Berlin-New York 1971. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Space
In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification. Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis. In geometric terms, a complete, simply connected Riemannian manifold is a symmetric space if and only if its curvature tensor is invariant under parallel transport. More generally, a Riemannian manifold (''M'', ''g'') is said to be symmetric if and only if, for each point ''p'' of ''M'', there exists an isometry of ''M'' fixing ''p'' and acting on the tangent space T_pM as minus the identity (every symmetric space is complete, since any geodesic can be extended indefinitely via symmetries about t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin(7)-manifold
In mathematics, a Spin(7)-manifold is an eight-dimensional Riemannian manifold whose holonomy group is contained in Spin(7). Spin(7)-manifolds are Ricci-flat and admit a parallel spinor. They also admit a parallel 4-form, known as the Cayley form, which is a calibrating form for a special class of submanifolds called Cayley cycles. History The fact that Spin(7) might possibly arise as the holonomy group of certain Riemannian 8-manifolds was first suggested by the 1955 classification theorem of Marcel Berger, and this possibility remained consistent with the simplified proof of Berger's theorem given by Jim Simons in 1962. Although not a single example of such a manifold had yet been discovered, Edmond Bonan then showed in 1966 that, if such a manifold did in fact exist, it would carry a parallel 4-form, and that it would necessarily be Ricci-flat. The first local examples of 8-manifolds with holonomy Spin(7) were finally constructed around 1984 by Robert Bryant, and his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quaternion-Kähler Manifold
In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(''n'')·Sp(1) for some n\geq 2. Here Sp(''n'') is the sub-group of SO(4n) consisting of those orthogonal transformations that arise by left-multiplication by some quaternionic n \times n matrix, while the group Sp(1) = S^3 of unit-length quaternions instead acts on quaternionic n-space ^n = ^ by right scalar multiplication. The Lie group Sp(n)\cdot Sp(1) \subset SO(4n) generated by combining these actions is then abstractly isomorphic to p(n) \times Sp(1) _2. Although the above loose version of the definition includes hyperkähler manifolds, the standard convention of excluding these will be followed by also requiring that the scalar curvature be non-zero— as is automatically true if the holonomy group equals the entire group Sp(''n'')·Sp(1). Early history Marcel Berger's 1955 paper on the classifica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametrix
In mathematics, and specifically the field of partial differential equations (PDEs), a parametrix is an approximation to a fundamental solution of a PDE, and is essentially an approximate inverse to a differential operator. A parametrix for a differential operator is often easier to construct than a fundamental solution, and for many purposes is almost as good. It is sometimes possible to construct a fundamental solution from a parametrix by iteratively improving it. Overview and informal definition It is useful to review what a fundamental solution for a differential operator with constant coefficients is: it is a distribution on ℝ''n'' such that :P(D) = \delta(x)~, in the weak sense, where is the Dirac delta distribution. In a similar way, a parametrix for a variable coefficient differential operator is a distribution such that :P(x,D) = \delta(x) + \omega(x) ~, where is some function with compact support. The parametrix is a useful concept in the study of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Isomorphism
In mathematics—more specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle \mathrmM and the cotangent bundle \mathrm^* M of a pseudo-Riemannian manifold induced by its metric tensor. There are similar isomorphisms on symplectic manifolds. The term ''musical'' refers to the use of the symbols \flat (flat) and \sharp (sharp). In covariant and contravariant notation, it is also known as raising and lowering indices. Motivation In linear algebra, a finite-dimensional vector space is isomorphic to its dual but not canonically isomorphic to it. On the other hand a Euclidean vector space, i.e., a finite-dimensional vector space E endowed with an inner product \langle\cdot,\cdot\rangle, is canonically isomorphic to its dual, the isomorphism being given by: \left\} is a moving tangent frame (see also smooth frame) for the ''tangent bundle'' with, as dual frame (see also dual basis), the moving cof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Besse
Arthur Besse is a pseudonym chosen by a group of French differential geometers, led by Marcel Berger, following the model of Nicolas Bourbaki. A number of monographs have appeared under the name. Bibliography * ** *Actes de la Table Ronde de Géométrie Différentielle. roceedings of the Roundtable on Differential GeometryEn l'honneur de Marcel Berger. n honor of Marcel BergerHeld in Luminy, July 12–18, 1992. Edited by Arthur L. Besse. Séminaires et Congrès eminars and Congresses 1. Société Mathématique de France, Paris; distributed by American Mathematical Society, Providence, RI, 1996. *Besse, Arthur L.: Some trends in Riemannian geometry. Duration and change, 71–105, Springer, Berlin, 1994 . *Besse, A. Многообразия Эйнштейна. Том I,II. (Russian) instein manifolds. Vol. I, IITranslated from the English and with a preface by D. V. Alekseevskiĭ. "Mir", Moscow, 1990. Vol. I: 320 pp.; Vol. II: pp. 321–704. *Besse, Arthur L.: E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graduate Texts In Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages). The GTM series is easily identified by a white band at the top of the book. The books in this series tend to be written at a more advanced level than the similar Undergraduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. List of books #''Introduction to Axiomatic Set Theory'', Gaisi Takeuti, Wilson M. Zaring (1982, 2nd ed., ) #''Measure and Category – A Survey of the Analogies between Topological and Measure Spaces'', John C. Oxtoby (1980, 2nd ed., ) #''Topological Vector Spaces'', H. H. Schaefer, M. P. Wolff (1999, 2nd ed., ) #''A Course in Homological Algebra'', Peter Hilton, Urs Stammbac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systolic Geometry
In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in its arithmetical, ergodic, and topological manifestations. See also a slower-paced Introduction to systolic geometry. The notion of systole The ''systole'' of a compact metric space ''X'' is a metric invariant of ''X'', defined to be the least length of a noncontractible loop in ''X'' (i.e. a loop that cannot be contracted to a point in the ambient space ''X''). In more technical language, we minimize length over free loops representing nontrivial conjugacy classes in the fundamental group of ''X''. When ''X'' is a graph, the invariant is usually referred to as the girth, ever since the 1947 article on girth by W. T. Tutte. Possibly inspired by Tutte's article, Loewner started thinking about systolic questions on surfaces in the la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lester R
Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include: People Given name * Lester Bangs (1948–1982), American music critic * Lester W. Bentley (1908–1972), American artist from Wisconsin * Lester Bird (1938–2021), second prime minister of Antigua and Barbuda (1994–2004) * Lester Cotton (born 1996), American football player * Lester del Rey (1915–1993), American science fiction author and editor * Lester Flatt (1914–1979), American bluegrass musician * Lester Gillis (1908–1934), better known as Baby Face Nelson, American gangster * Lester Holt (born 1959), American television journalist * Lester Charles King (1907–1989), English geomorphologist * Lester Lanin (1907–2004), American jazz and pop music bandleader * Lester Lockett (1912–2005), American Negro League baseball player * Lester Maddox (1915–2003), governor and lieutenant governor of the U.S. state of Georgia * Lester Patrick (1883–1960), Can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Société Mathématique De France
Lactalis is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier SA. Lactalis is the largest dairy products group in the world, and is the second largest food products group in France, behind Danone. It owns brands such as Parmalat, Président, Siggi's Dairy, Skånemejerier, Rachel's Organic, and Stonyfield Farm. History André Besnier started a small cheesemaking company in 1933 and launched its ''Président'' brand of Camembert in 1968. In 1990, it acquired Group Bridel (2,300 employees, 10 factories, fourth-largest French dairy group) with a presence in 60 countries. In 1992, it acquired United States cheese company Sorrento. In 1999, ''la société Besnier'' became ''le groupe Lactalis'' owned by Belgian holding company BSA International SA. In 2006, they bought Italian group Galbani, and in 2008, bought Swiss cheesemaker Baer. They bought Italian group Parmalat in a 2011 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
