Jump to content
 







Main menu
   


Navigation  



Main page
Contents
Current events
Random article
About Wikipedia
Contact us
Donate
 




Contribute  



Help
Learn to edit
Community portal
Recent changes
Upload file
 








Search  

































Create account

Log in
 









Create account
 Log in
 




Pages for logged out editors learn more  



Contributions
Talk
 



















Contents

   



(Top)
 


1 Life  





2 Selected works  





3 References  





4 External links  














Solomon Lefschetz






العربية
Català
Deutsch
Español
فارسی
Français

Bahasa Indonesia
Italiano
עברית
Kreyòl ayisyen
مصرى
Nederlands

Norsk nynorsk
Piemontèis
Polski
Português
Русский
Slovenščina
Türkçe
Українська
Tiếng Vit

 

Edit links
 









Article
Talk
 

















Read
Edit
View history
 








Tools
   


Actions  



Read
Edit
View history
 




General  



What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Cite this page
Get shortened URL
Download QR code
Wikidata item
 




Print/export  



Download as PDF
Printable version
 




In other projects  



Wikimedia Commons
Wikiquote
 
















Appearance
   

 






From Wikipedia, the free encyclopedia
 


Solomon Lefschetz
Born(1884-09-03)3 September 1884
Died5 October 1972(1972-10-05) (aged 88)
CitizenshipUS
Alma materÉcole Centrale Paris
Clark University
Known forLefschetz 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
AwardsBôcher Memorial Prize (1924)
National Medal of Science (1964)
Leroy P. Steele Prize (1970)
Fellow of the Royal Society[1]
Scientific career
FieldsAlgebraic topology
Institutions
  • University of Kansas
  • Princeton University
  • National Autonomous University of Mexico[2]
  • Brown University
  • ThesisOn the Existence of Loci with Given Singularities (1911)
    Doctoral advisorWilliam Edward Story[3]
    Doctoral studentsEdward 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 studentsSylvia de Neymet

    Solomon Lefschetz ForMemRS (Russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.[3][1][4][5]

    Life[edit]

    He was born in Moscow, 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 held Ottoman passports)[citation needed]. Shortly thereafter, the family moved to Paris. He was educated there in engineering at the École 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 a Ph.D. in algebraic geometry from Clark University in Worcester, Massachusetts in 1911.[7] 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 Paris. 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. He was an Invited Speaker of the ICM in 1920 in Strasbourg.[8] 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 SGA 7 also for the study of Picard groupsofZariski surface). In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. He was elected to the United States National Academy of Sciences in 1925 and the American Philosophical Society in 1929.[9][10]

    The Lefschetz fixed-point theorem, now a basic result of topology, was developed by him 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 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, the Annals 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 the National 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 of Sputnik, to augment the mathematical component of Glenn L. Martin Company's Research Institute for Advanced Studies (RIAS) in Baltimore, Maryland. His team became the world's largest group of mathematicians devoted to research in nonlinear 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 at Brown University, Providence, Rhode Island.[13]

    Selected works[edit]

    References[edit]

    1. ^ a b Hodge, W. V. D. (1973). "Solomon Lefschetz 1884-1972". Biographical Memoirs of Fellows of the Royal Society. 19: 433–453. doi:10.1098/rsbm.1973.0016. S2CID 122747688.
  • ^ a b "Mathematics in Mexico" (PDF). Sociedad Matematica Mexicana.
  • ^ a b c Solomon Lefschetz at the Mathematics Genealogy Project
  • ^ Markus, L. (1973). "Solomon Lefschetz: An appreciation in memoriam". Bull. Amer. Math. Soc. 79 (4): 663–680. doi:10.1090/s0002-9904-1973-13256-2.
  • ^ O'Connor, John J.; Robertson, Edmund F., "Solomon Lefschetz", MacTutor History of Mathematics Archive, University of St Andrews
  • ^ Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical, p. 148, at Google Books
  • ^ Lefschetz, Solomon (1911). On the existence of LocI with given singularities (Ph.D.). Clark University. OCLC 245921866 – via ProQuest.
  • ^ "Quelques remarques sur la multiplication complexe by S. Lefschetz" (PDF). Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920. 1921. pp. 300–307. Archived from the original (PDF) on 2017-10-29.
  • ^ "Solomon Lefschetz". www.nasonline.org. Retrieved 2023-07-20.
  • ^ "APS Member History". search.amphilsoc.org. Retrieved 2023-07-20.
  • ^ a b Griffiths, Phillip; Spencer, Donald; Whitehead, George (1992). "Solomon Lefschetz 1884-1972" (PDF). National Academy of Sciences. Archived from the original (PDF) on 2014-12-22.
  • ^ Allen, K. N. (1988, January). Undaunted genius. Clark News, 11(1), p. 9.
  • ^ About LCDS (Lefschetz Center for Dynamical Systems @ Brown University)
  • ^ Alexander, James W. (1925). "Review: S. Lefschetz, L'Analysis Situs et la Géométrie Algébrique". Bull. Amer. Math. Soc. 31 (9): 558–559. doi:10.1090/s0002-9904-1925-04116-6.
  • ^ Zariski, Oscar (1930). "Review: S. Lefschetz, Géométrie sur les Surfaces et les Variétés Algébriques". Bulletin of the American Mathematical Society. 36 (9): 617–618. doi:10.1090/s0002-9904-1930-05017-x.
  • ^ Smith, Paul A. (1931). "Letschetz on Topology". Bulletin of the American Mathematical Society. 37 (9, Part 1): 645–648. doi:10.1090/S0002-9904-1931-05201-0.
  • ^ Antosiewicz, H. A. (1963). "Review: Joseph LaSalle and Solomon Lefschetz, Stability by Liapunov's direct method with applications". Bulletin of the American Mathematical Society. 69 (2): 209–210. doi:10.1090/s0002-9904-1963-10915-5.
  • ^ Haas, Felix (1958). "Review: S. Lefschetz, Differential equations: Geometric theory". Bulletin of the American Mathematical Society. 64 (4): 203–206. doi:10.1090/s0002-9904-1958-10212-8.
  • External links[edit]


    Retrieved from "https://en.wikipedia.org/w/index.php?title=Solomon_Lefschetz&oldid=1217696895"

    Categories: 
    1884 births
    1972 deaths
    American topologists
    École Centrale Paris alumni
    Jewish American scientists
    Russian Jews
    Emigrants from the Russian Empire to the United States
    20th-century American mathematicians
    Princeton University faculty
    Clark University alumni
    National Medal of Science laureates
    Foreign Members of the Royal Society
    University of Kansas faculty
    Presidents of the American Mathematical Society
    Brown University faculty
    Members of the American Philosophical Society
    Hidden categories: 
    Articles with short description
    Short description is different from Wikidata
    Articles with hCards
    Pages using Template:Post-nominals with missing parameters
    Pages using Template:Post-nominals with customized linking
    Articles containing Russian-language text
    All articles with unsourced statements
    Articles with unsourced statements from March 2020
    Articles with Internet Archive links
    Articles with LibriVox links
    Articles with FAST identifiers
    Articles with ISNI identifiers
    Articles with VIAF identifiers
    Articles with WorldCat Entities identifiers
    Articles with BIBSYS identifiers
    Articles with BNF identifiers
    Articles with BNFdata identifiers
    Articles with GND identifiers
    Articles with ICCU identifiers
    Articles with J9U identifiers
    Articles with LCCN identifiers
    Articles with Libris identifiers
    Articles with NDL identifiers
    Articles with NKC identifiers
    Articles with NLA identifiers
    Articles with NTA identifiers
    Articles with PLWABN identifiers
    Articles with CINII identifiers
    Articles with MATHSN identifiers
    Articles with MGP identifiers
    Articles with Scopus identifiers
    Articles with ZBMATH identifiers
    Articles with DTBIO identifiers
    Articles with Trove identifiers
    Articles with SNAC-ID identifiers
    Articles with SUDOC identifiers
     



    This page was last edited on 7 April 2024, at 09:58 (UTC).

    Text is available under the Creative Commons Attribution-ShareAlike License 4.0; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.



    Privacy policy

    About Wikipedia

    Disclaimers

    Contact Wikipedia

    Code of Conduct

    Developers

    Statistics

    Cookie statement

    Mobile view



    Wikimedia Foundation
    Powered by MediaWiki