| Solomon Lefschetz | |
| Born | September 3, 1884 Moscow, Russia |
|---|---|
| Died | October 5, 1972 |
| Residence | USA |
| Nationality | Russian |
| Ethnicity | Jewish |
| Fields | algebraic topology |
| Institutions | University of Nebraska University of Kansas Princeton University |
| Alma mater | Ecole Centrale Paris |
| Doctoral advisor | William Edward Story,Clark University |
| 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 |
| Known for | Lefschetz fixed point theorem, Picard-Lefschetz formula |
| Notable awards | Bôcher Memorial Prize |
Solomon Lefschetz (3 September 1884 – 5 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. Moscow (Москва́ romanised: Moskvá, IPA: see also other names) is the Capital and the largest city of Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending The University of Nebraska is the public University system in the state of Nebraska, USA. The University of Kansas (often referred to as KU or just Kansas) is a public research university with campuses located in Lawrence, Kansas City Princeton University is a private Coeducational research university located in Princeton, New Jersey. Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval École Centrale Paris is a renowned French university-level institution ( Grande Ecole) in the field of Engineering. A doctorate is an Academic degree that indicates the highest level of academic achievement William Edward Story (* April 29, 1850 in Boston, Massachusetts, U Clark University is a private University and Liberal arts college in Worcester Massachusetts. Edward Griffith Begle ( 27 November 1914 - 2 March 1978) was a Mathematician best known for his role as the director of the School Richard Ernest Bellman ( August 26, 1920 – March 19, 1984) was an applied mathematician, celebrated for his invention of Felix E Browder (1927- is a United States Mathematician. He is the eldest son of Earl Browder and brother of William Browder. Clifford Hugh Dowker (1912-1982 was a Topologist known for his work in Point-set topology and also for his contributions in Category theory, Sheaf Ralph Hartzler Fox ( March 24, 1913, Morrisville Pennsylvania &ndash December 23, 1973, Philadelphia) was an Trained as a mathematician Dr Ralph E Gomory first became a researcher and then an executive at IBM John McCarthy (born September 4, 1927, in Boston, Massachusetts) is an American Computer scientist and Cognitive Robert Clay Prim (born 1921 in Sweetwater, Texas) is an American Mathematician and Computer scientist. Paul Althaus Smith was an American mathematician His name occurs in two significant conjectures in Geometric topology: the Smith conjecture, which is now Norman Earl Steenrod ( April 22, 1910 – October 14, 1971) was a preeminent Mathematical Topologist who most widely known for his contributions Clifford Ambrose Truesdell III, ( February 18, 1919 &ndash January 14, 2000) was an American Mathematician, Natural philosopher Albert William Tucker ( 28 November 1905 – 25 January, 1995) was a Canadian-born American Mathematician who made important John Wilder Tukey ( June 16, 1915 &ndash July 26, 2000) was an American Statistician. Henry (Hank Wallman (1915 – 1992 was an American mathematician known for his work in Lattice theory, Dimension theory, Topology, and Electronic Shaun Wylie (born 17 January 1913) is a British Mathematician and former World War II codebreaker In Mathematics, the Lefschetz fixed-point theorem is a formula that counts the number of fixed points of a continuous mapping from a compact The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1450 (contributed by Events 36 BC - In the Battle of Naulochus, Marcus Vipsanius Agrippa, Admiral of Octavian, defeats Sextus Pompeius Year 1884 ( MDCCCLXXXIV) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Leap year Events 869 - The Fourth Council of Constantinople is convened to decide about what to do about Patriarch Photius of Constantinople Year 1972 ( MCMLXXII) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar. The United States of America —commonly referred to as the A mathematician is a person whose primary area of study and research is the field of Mathematics. Algebraic topology is a branch of Mathematics which uses tools from Abstract algebra to study Topological spaces The basic goal is to find algebraic Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with In Mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one Independent variable, and one or more of its
Contents |
Life
He was born in Moscow into a Jewish family (his parents were Turkish citizens) who moved shortly after that to Paris. Moscow (Москва́ romanised: Moskvá, IPA: see also other names) is the Capital and the largest city of PLEASE TAKE NOTE************ Turkey (Türkiye known officially as the Republic of Turkey ( is a Eurasian Country that stretches Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city He was educated there in engineering at Ecole Centrale Paris, but emigrated to the USA in 1905. Engineering is the Discipline and Profession of applying technical and scientific Knowledge and École Centrale Paris is a renowned French university-level institution ( Grande Ecole) in the field of Engineering.
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. Clark University is a private University and Liberal arts college in Worcester Massachusetts. 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. The University of Nebraska is the public University system in the state of Nebraska, USA. The University of Kansas (often referred to as KU or just Kansas) is a public research university with campuses located in Lawrence, Kansas City Princeton University is a private Coeducational research university located in Princeton, New Jersey. 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 Ecole Centrale. Charles Émile Picard (usually referred to simply as Émile Picard) ( July 24, 1856 - December 12, 1941) was a leading French Centrale Graduate School is the group formed by the following Graduate Schools of Engineering: École centrale Paris established in 1829 École 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). A hyperplane is a concept in Geometry. It is a higher-dimensional generalization of the concepts of a line in Euclidean plane geometry and a "Morse function" redirects here In another context a "Morse function" can also mean an Anharmonic oscillator. In Mathematics, a Lefschetz pencil is a construction in Algebraic geometry considered by Solomon Lefschetz, in order to analyse the Algebraic topology 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. In Mathematics, vanishing cycles are studied in Singularity theory and other part of Algebraic geometry. for the degeneracy of a Graph, see Arboricity#Related_concepts. In Mathematics, monodromy is the study of how objects from Mathematical analysis, Algebraic topology and algebraic and Differential geometry 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 Mathematics, homology theory is the Axiomatic study of the intuitive geometric idea of homology of cycles on Topological spaces It can be broadly In Mathematics, the Weil conjectures, which had become theorems by 1974 were some highly-influential proposals from the late 1940s by André Weil on the In Mathematics, Alexander Grothendieck 's Séminaire de géométrie algébrique was a unique phenomenon of research and publication outside of the main Mathematical In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. Year 1924 ( MCMXXIV) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian calendar. The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1450 (contributed by
The Lefschetz fixed point theorem, now a basic result of topology, he developed in papers from 1923 to 1927, initially for manifolds. In Mathematics, the Lefschetz fixed-point theorem is a formula that counts the number of fixed points of a continuous mapping from a compact A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be 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. In Mathematics, specifically in Algebraic topology, cohomology is a general term for a Sequence of Abelian groups defined from a Cochain In Mathematics, the concept of intersection number arose in Algebraic geometry, where two curves intersecting at a point may be considered to 'meet twice' if they In Mathematics, specifically in Algebraic topology, the cup product is a method of adjoining two Cocycles of degree p and q to form His work on topology was summed up in his monograph Algebraic Topology (1942). From 1944 he worked on differential equations. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the
He was editor of the Annals of Mathematics from 1928 to 1958. The Annals of Mathematics (ISSN 0003-486X abbreviated as Ann of Math 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.
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. The Glenn L Martin Company was an early US Aircraft company founded by aviation pioneer Glenn Luther Martin. His team became the world's largest group of mathematicians devoted to research in nonlinear differential equations. [1] 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. Brown University is a highly esteemed private University located in Providence, Rhode Island and is a member of the Ivy League. [1]
See also
References
- ^ Allen, K. In Mathematics, the Lefschetz hyperplane theorem states that a Hyperplane section W of a Non-singular Complex algebraic variety In Mathematics, Lefschetz duality is a version of Poincaré duality in Geometric topology, applying to a Manifold with boundary. N. (1988, January). Undaunted genius. Clark News, 11(1), p. 9.
External links
- O'Connor, John J. & Robertson, Edmund F. , “Solomon Lefschetz”, MacTutor History of Mathematics archive
- Solomon Lefschetz at the Mathematics Genealogy Project
- "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. The MacTutor History of Mathematics archive is an award-winning website maintained by John J The Mathematics Genealogy Project is a web-based Database that gives an Academic genealogy based on Dissertation supervision relations
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