Solomon Lefschetz | |
|---|---|
 | |
| Born | (1884-09-03)3 September 1884 |
| Died | 5 October 1972(1972-10-05) (aged 88) |
| Citizenship | US |
| Alma mater | École Centrale Paris Clark University |
| Known for | Lefschetz fixed-point theorem Picard–Lefschetz theory Lefschetz connection Lefschetz hyperplane theorem Lefschetz duality Lefschetz manifold Lefschetz number Lefschetz principle Lefschetz zeta function Lefschetz pencil Lefschetz theorem on (1,1)-classes |
| Awards | Bôcher Memorial Prize(1924) National Medal of Science(1964) Leroy P. Steele Prize(1970) Fellow of the Royal Society[1] |
| Scientific career | |
| Fields | Algebraic topology |
| Institutions | |
| Thesis | On the Existence of Loci with Given Singularities (1911) |
| Doctoral advisor | William Edward Story[3] |
| Doctoral students | Edward Begle Richard Bellman Felix Browder Clifford Dowker George F. D. Duff Ralph Fox Ralph Gomory John McCarthy Robert Prim Paul A. Smith Norman Steenrod Arthur Harold Stone Clifford Truesdell Albert W. Tucker John Tukey Henry Wallman Shaun Wylie[3] |
| Other notable students | Sylvia de Neymet |
Solomon LefschetzForMemRS (Russian:Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was a Russian-born Americanmathematician who did fundamental work onalgebraic topology, its applications toalgebraic geometry, and the theory of non-linearordinary differential equations.[3][1][4][5]
He was born inMoscow, the son of Alexander Lefschetz and his wife Sarah or Vera Lifschitz, Jewish traders who used to travel around Europe and the Middle East (they heldOttoman passports).[5] Shortly thereafter, the family moved toParis. He was educated there inengineering at theÉcole Centrale Paris, but emigrated to the US in 1905.
He was badly injured in an industrial accident in 1907, losing both hands.[6] He moved towards mathematics, receiving aPh.D. in algebraic geometry fromClark University in Worcester, Massachusetts in 1911.[7] He then took positions at theUniversity of Nebraska andUniversity of Kansas, moving toPrinceton 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 ofCharles Émile Picard, whom he had heard lecture in Paris at theÉcole Centrale Paris. He proved theorems on the topology ofhyperplane sections ofalgebraic varieties, which provide a basic inductive tool (these are now seen as allied toMorse theory, though aLefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). ThePicard–Lefschetz formula in the theory ofvanishing cycles is a basic tool relating thedegeneration of families of varieties with 'loss' of topology, tomonodromy. He was an Invited Speaker of theICM in 1920 in Strasbourg.[8] His bookL'analysis situs et la géométrie algébrique from 1924, though opaque foundationally given the current technical state ofhomology theory, was in the long term very influential (one could say that it was one of the sources for the eventual proof of theWeil conjectures, throughSGA 7 also for the study ofPicard groups ofZariski surface). In 1924 he was awarded theBôcher Memorial Prize for his work inmathematical analysis. He was elected to the United StatesNational Academy of Sciences in 1925 and theAmerican Philosophical Society in 1929.[9][10]
TheLefschetz fixed-point theorem, now a basic result of topology, was developed by him in papers from 1923 to 1927, initially formanifolds. Later, with the rise ofcohomology theory in the 1930s, he contributed to theintersection number approach (that is, in cohomological terms, the ring structure) via thecup product and duality on manifolds. His work on topology was summed up in his monographAlgebraic Topology (1942). From 1944 he worked ondifferential equations.
He was editor of theAnnals of Mathematics from 1928 to 1958. During this time, theAnnals became an increasingly well-known and respected journal, and Lefschetz played an important role in this.[11]
In 1945 he travelled to Mexico for the first time, where he joined the Institute of Mathematics at theNational University of Mexico as a visiting professor. He visited frequently for long periods, and during 1953–1966 he spent most of his winters in Mexico City.[11] He played an important role in the foundation of mathematics in Mexico, and sent several students back to Princeton. His students included Emilio Lluis,José Adem,Samuel Gitler,Santiago López de Medrano,Francisco Javier González-Acuña and Alberto Verjovsky.[2]
Lefschetz came out of retirement in 1958, because of the launch ofSputnik, to augment the mathematical component ofGlenn L. Martin Company'sResearch Institute for Advanced Studies (RIAS) in Baltimore, Maryland. His team became the world's largest group of mathematicians devoted to research innonlinear differential equations.[12] The RIAS mathematics group stimulated the growth of nonlinear differential equations through conferences and publications. He left RIAS in 1964 to form the Lefschetz Center for Dynamical Systems atBrown University, Providence, Rhode Island.[13]
