Solomon Lefschetz

Solomon Lefschetz

Infobox Scientist
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name =Solomon Lefschetz


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birth_date = September 3, 1884
birth_place = Moscow, Russia
death_date = October 5, 1972
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residence = USA
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nationality = Russian
ethnicity = Jewish
fields = algebraic topology
workplaces = University of Nebraska
University of Kansas
Princeton University
alma_mater = École Centrale Paris
doctoral_advisor = William Edward Story,Clark University
academic_advisors =
doctoral_students = Edward Begle
Richard Bellman
Felix Browder
Clifford Dowker
Ralph Fox
Ralph Gomory
John McCarthy
Robert Prim
Paul A. Smith
Norman Steenrod
Clifford Truesdell
Albert W. Tucker
John Tukey
Henry Wallman
Shaun Wylie

notable_students =
known_for = Lefschetz fixed point theorem, Picard-Lefschetz formula
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awards = Bôcher Memorial Prize


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Solomon Lefschetz (3 September 18845 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.

Life

He was born in Moscow into a Jewish family (his parents were Turkish citizens) who moved shortly after that to Paris. He was educated there in engineering at the École Centrale Paris, but emigrated to the USA in 1905.

He was badly injured in an industrial accident in 1907, losing both hands. He moved towards mathematics, receiving a Ph.D. in algebraic geometry from Clark University in Worcester, Massachusetts in 1911. He then took positions in University of Nebraska and University of Kansas, moving to Princeton University in 1924, where he was soon given a permanent position. He remained there until 1953.

In the application of topology to algebraic geometry, he followed the work of Charles Émile Picard, whom he had heard lecture in Paris at the École Centrale. He proved theorems on the topology of hyperplane sections of algebraic varieties, which provide a basic inductive tool (these are now seen as allied to Morse theory, though a Lefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). The Picard-Lefschetz formula in the theory of vanishing cycles is a basic tool relating the degeneration of families of varieties with 'loss' of topology, to monodromy. His book "L'analysis situs et la géométrie algébrique" from 1924, though opaque foundationally given the current technical state of homology theory, was in the long term very influential (one could say that it was one of the sources for the eventual proof of the Weil conjectures, through SGA7). In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis.

The Lefschetz fixed point theorem, now a basic result of topology, he developed in papers from 1923 to 1927, initially for manifolds. Later, with the rise of cohomology theory in the 1930s, he contributed to the intersection number approach (that is, in cohomological terms, the ring structure) via the cup product and duality on manifolds. His work on topology was summed up in his monograph " [http://www.ams.org/online_bks/coll27/ Algebraic Topology] " (1942). From 1944 he worked on differential equations.

He was editor of "the Annals of Mathematics" from 1928 to 1958. During this time, "Annals" became an increasingly well-known and respected journal, and Lefschetz played an important role in this. The rise of "Annals", in turn, stimulated American mathematics.Fact|date=August 2008

Lefschetz came out of retirement in 1958, because of the launch of Sputnik, to augment the mathematical component of Glenn L. Martin Company’s Research Institute for Advanced Study (RIAS) in Baltimore, Maryland. His team became the world's largest group of mathematicians devoted to research in nonlinear differential equations. [Allen, K. N. (1988, January). Undaunted genius. "Clark News", 11(1), p. 9.] The RIAS mathematics group stimulated the growth of nonlinear differential equations through conferences and publications. It left RIAS in 1964 to form the Lefschetz Center for Dynamical Systems at Brown University, Providence, Rhode Island. [http://www.dam.brown.edu/lcds/about.php]

ee also

*Lefschetz hyperplane theorem
*Lefschetz duality

References

External links

*MacTutor Biography|id=Lefschetz
*
* [http://libweb.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pmcxrota.htm "Fine Hall in its golden age: Remembrances of Princeton in the early fifties" by Gian-Carlo Rota.] Contains a lengthy section on Lefschetz at Princeton.


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  • Solomon Lefschetz — Solomon Lefschetz, (* 3. September 1884 in Moskau; † 5. Oktober 1972 in Princeton, New Jersey, USA) war ein US amerikanischer Mathematiker, der vor allem auf dem Gebiet der Topologie und der Differentialgleichungen arbeitete. Leben und Werk Seine …   Deutsch Wikipedia

  • Solomon Lefschetz — (3 septembre 1884 5 octobre 1972) était un mathématicien américain. Né à Moscou dans une famille juive, étudiant à Paris à l Ecole centrale des arts et manufactures puis aux États Unis où il obtint un PhD de l Université Clark à Worcester… …   Wikipédia en Français

  • Solomon Lefschetz — (3 de septiembre de 1884 5 de octubre de 1972), ingeniero y matemático estadounidense de origen ruso, pionero en el desarrollo de las técnicas algebraicas de topología, palabra que él creó en 1930. Biografía Nació en Moscú y estudió en París y en …   Wikipedia Español

  • Solomon Lefschetz — (1884 1972), ingeniero y matemático estadounidense de origen ruso, pionero en el desarrollo de las técnicas algebraicas de topología, palabra que él creó en 1930 …   Enciclopedia Universal

  • Lefschetz — Solomon Lefschetz, (* 3. September 1884 in Moskau; † 5. Oktober 1972 in Princeton, New Jersey, USA) war ein US amerikanischer Mathematiker, der vor allem auf dem Gebiet der Topologie und der Differentialgleichungen arbeitete. Leben und Werk Seine …   Deutsch Wikipedia

  • LEFSCHETZ (S.) — LEFSCHETZ SOLOMON (1884 1972) Mathématicien américain d’origine russe, Solomon Lefschetz fut le créateur de la topologie algébrique et a apporté d’importantes contributions à la géométrie algébrique. Né à Moscou, Lefschetz fit ses études à… …   Encyclopédie Universelle

  • Lefschetz fixed-point theorem — In mathematics, the Lefschetz fixed point theorem is a formula that counts the number of fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X . It …   Wikipedia

  • Lefschetz pencil — In mathematics, a Lefschetz pencil is a construction in algebraic geometry considered by Solomon Lefschetz, in order to analyse the algebraic topology of an algebraic variety V . A pencil here is a particular kind of linear system of divisors on… …   Wikipedia

  • Lefschetz hyperplane theorem — In mathematics, the Lefschetz hyperplane theorem states that a hyperplane section W of a non singular complex algebraic variety V , in complex projective space, inherits most of its algebraic topology from V . This allows certain geometrical… …   Wikipedia

  • Lefschetz duality — In mathematics, Lefschetz duality is a version of Poincaré duality in geometric topology, applying to a manifold with boundary. Such a formulation was introduced by Solomon Lefschetz in the 1920s, at the same time introducing relative homology,… …   Wikipedia

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