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Lucien Szpiro

December 28, 2022

Lucien Serge Szpiro (23 December 1941 – 18 April 2020) was a French mathematician known for his work in number theory, arithmetic geometry, and commutative algebra. He formulated Szpiro's conjecture and was a Distinguished Professor at the CUNY Graduate Center and an emeritus Director of Research [fr] at the CNRS.

Lucien Serge Szpiro
Born(1941-12-23)23 December 1941
Paris, France
Died18 April 2020(2020-04-18) (aged 78)
Paris, France
NationalityFrench
Alma materParis-Sud University
Known forSzpiro's conjecture
AwardsPrix Doistau–Blutel (1987)
Fellow of the American Mathematical Society (2012)
Member of the Academia Europaea
Scientific career
FieldsMathematics
InstitutionsCity University of New York
CNRS
Doctoral advisorPierre Samuel
Doctoral studentsAhmed Abbes
Emmanuel Ullmo
Shou-Wu Zhang
InfluencesMaurice Auslander
Claude Chevalley
Alexander Grothendieck

Early life and education

Lucien Serge Szpiro was born on 23 December 1941 in the 20th arrondissement of Paris, France.[1][2] Szpiro attended Paris-Sud University where he earned his Ph.D. under Pierre Samuel.[1][3] His doctoral work was heavily influenced by the seminars of Maurice Auslander, Claude Chevalley, and Alexander Grothendieck.[1] He earned his Doctorat d'État (DrE) in 1971.[1]

Career

From 1963 to 1965, Szpiro worked as an assistant high school teacher in Paris.[1][4] From 1965 to 1969, he was an assistant professor (maître assistant) at the University of Paris.[1][4] From 1969 to 1999, Szpiro worked at the CNRS, initially as an attaché at Paris Diderot University before rising to the rank of a distinguished professor (Directeur de Recherche de Classe Exceptionnelle) at Paris-Sud University.[4] In 1999, he became an emeritus professor (Directeur de Recherche émérite) at the CNRS and moved to the CUNY Graduate Center as a Distinguished Professor.[1][4][5] He also held visiting positions at several institutions including Columbia University and the Institute for Advanced Study.[4][6]

Szpiro was the editor-in-chief of Astérisque from 1991 to 1993 and an editor of the Bulletin de la Société Mathématique de France from 1984 to 1990.[1] He was also head of the commission that oversaw the Société mathématique de France libraries.[7]

Szpiro advised 17 doctoral students, including Ahmed Abbes, Emmanuel Ullmo, and Shou-Wu Zhang.[1][3]

Research

In the 1970s, Szpiro's research in commutative algebra led to his proof of the Auslander zero divisor conjecture.[8] Together with Christian Peskine, he developed the liaison theory of algebraic varieties.[8]

In the 1980s, Szpiro's research interests shifted to Diophantine geometry, first over function fields and then over number fields.[8] The Institut des hautes études scientifiques described Szpiro as being "the first to realise the importance of a paper by Arakelov for questions of Diophantine geometry", which ultimately led to the development of Arakelov theory as a tool of modern Diophantine geometry exemplified by Gerd Faltings's proof of the Mordell conjecture.[5][8] Szpiro also showed the link between the positivity of the dualising sheaf of a curve and the Bogomolov conjecture.[8]

In 1981, Szpiro formulated a conjecture (now known as Szpiro's conjecture) relating the discriminant of an elliptic curve with its conductor.[9] His conjecture inspired the abc conjecture,[10] which was later shown to be equivalent to a modified form of Szpiro's conjecture in 1988.[11] Szpiro's conjecture and its equivalent forms have been described as "the most important unsolved problem in Diophantine analysis" by Dorian Goldfeld,[12] in part to its large number of consequences in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem.[13][14][15][16]

After moving to the CUNY Graduate Center in 1999, Szpiro began working on new research in algebraic dynamics.[5][8]

Awards

In 1987, Szpiro received the Prix Doistau–Blutel from the French Academy of Sciences "for his work in Commutative Algebra and Algebraic Geometry and for his contribution to G. Faltings’ proof of the Mordell conjecture."[5] In 2012 he became a fellow of the American Mathematical Society.[17] He was a Member of the Academia Europaea.[4]

Death

Szpiro died on 18 April 2020 in Paris, France, from cardiac arrest.[18][8]

Selected publications

  • Pesenti, Jerome; Szpiro, Lucien (2000). "Inégalité du discriminant pour les pinceaux elliptiques à réductions quelconques". Compositio Mathematica. 120 (1): 83–117. doi:10.1023/A:1001736823128.
  • Peskine, Christian; Szpiro, Lucien (1973). "Dimension projective finie et cohomologie locale: Applications à la démonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck". Publications Mathématiques de l'IHÉS (in French). 42 (1): 47–119. doi:10.1007/BF02685877. ISSN 0073-8301. S2CID 124116905.
  • Peskine, Christian; Szpiro, Lucien (1974). "Liaison des variétés algébriques I". Inventiones Mathematicae (in French). 26 (4): 271–302. Bibcode:1974InMat..26..271P. doi:10.1007/BF01425554. ISSN 0020-9910. S2CID 123364655.
  • Szpiro, Lucien; Ullmo, Emmanuel; Zhang, Shou-Wu (1997). "Equirépartition des petits points". Inventiones Mathematicae (in French). 127 (2): 337–347. Bibcode:1997InMat.127..337S. doi:10.1007/s002220050123. S2CID 119668209.
  • Szpiro, Lucien (1979). "Sur le théorème de rigidité de Parsin et Arakelov". Astérisque. Journées de géométrie algébrique de Rennes - (Juillet 1978) (II) : Groupes formels, représentations galoisiennes et cohomologie des variétés de caractéristique positive. 64: 169–202. MR 0563470.
  • Szpiro, Lucien (1981). "Seminaire sur les pinceaux des courbes de genre au moins deux". Astérisque. 86 (3): 44–78. Zbl 0463.00009.
  • Szpiro, Lucien (1987). "Présentation de la théorie d'Arakelov". In Ribet, Kenneth A. (ed.). Current Trends in Arithmetical Algebraic Geometry. Contemporary Mathematics. Vol. 67. pp. 279–293. doi:10.1090/conm/067/902599. ISBN 9780821850749. Zbl 0634.14012.
  • Szpiro, Lucien. Conjecture de Mordell, Séminaire Nicolas Bourbaki 1983/4.

References

  1. ^ a b c d e f g h i "Curriculum Vitae" (PDF). 2010. Retrieved 19 April 2020.
  2. ^ "Fichiers des personnes décédées depuis 1970". Fichier des personnes décédées (in French). {{cite web}}: Missing or empty |url= (help)
  3. ^ a b Lucien Szpiro at the Mathematics Genealogy Project
  4. ^ a b c d e f "Lucien Szpiro". Academia Europaea. Retrieved 18 April 2020.
  5. ^ a b c d "Lucien Szpiro". Graduate Center, CUNY. Retrieved 18 April 2020.
  6. ^ "Lucien Szpiro". Institute for Advanced Study. 9 December 2019. Retrieved 19 April 2020.
  7. ^ "Un réseau de biblithèques spécialisées: le réseau des bibliothèques de mathematiques" (PDF). École Nationale Supérieure des Sciences de l'Information et des Bibliothèques (in French). 1992. Retrieved 19 April 2020. Lucien Szpiro, responsable de la commission des bibliothèques de la SMF, estime que le cout de l'operation serait de 100 000 francs par an pour un reseau ne contenant que des listes de livres et de preprints.
  8. ^ a b c d e f g "Mathematician Lucien Szpiro passed away at the age of 78". Institut des hautes études scientifiques. 20 April 2020. Retrieved 21 December 2020.
  9. ^ Lang, Serge (1997). Survey of Diophantine geometry. Berlin: Springer-Verlag. p. 51. ISBN 3-540-61223-8. Zbl 0869.11051.
  10. ^ Fesenko, Ivan (2015). "Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki" (PDF). European Journal of Mathematics. 1 (3): 405–440. doi:10.1007/s40879-015-0066-0. S2CID 52085917..
  11. ^ Oesterlé, Joseph (1988). "Nouvelles approches du "théorème" de Fermat". Astérisque. Séminaire Bourbaki exp 694 (161): 165–186. ISSN 0303-1179. MR 0992208.
  12. ^ Goldfeld, Dorian (1996). "Beyond the last theorem". Math Horizons. 4 (September): 26–34. doi:10.1080/10724117.1996.11974985. JSTOR 25678079.
  13. ^ Bombieri, Enrico (1994). "Roth's theorem and the abc-conjecture". Preprint. ETH Zürich.
  14. ^ Elkies, N. D. (1991). "ABC implies Mordell". International Mathematics Research Notices. 1991 (7): 99–109. doi:10.1155/S1073792891000144.
  15. ^ Pomerance, Carl (2008). "Computational Number Theory". The Princeton Companion to Mathematics. Princeton University Press. pp. 361–362.
  16. ^ Dąbrowski, Andrzej (1996). "On the diophantine equation x! + A = y2". Nieuw Archief voor Wiskunde, IV. 14: 321–324. Zbl 0876.11015.
  17. ^ List of Fellows of the American Mathematical Society, retrieved 5 August 2013.
  18. ^ "Lucien Szpiro 1941–2020 | Not Even Wrong".

External links

December 28, 2022
lucien, szpiro, lucien, serge, szpiro, december, 1941, april, 2020, french, mathematician, known, work, number, theory, arithmetic, geometry, commutative, algebra, formulated, szpiro, conjecture, distinguished, professor, cuny, graduate, center, emeritus, dire. Lucien Serge Szpiro 23 December 1941 18 April 2020 was a French mathematician known for his work in number theory arithmetic geometry and commutative algebra He formulated Szpiro s conjecture and was a Distinguished Professor at the CUNY Graduate Center and an emeritus Director of Research fr at the CNRS Lucien Serge SzpiroSzpiro at the Mathematical Research Institute of OberwolfachBorn 1941 12 23 23 December 1941Paris FranceDied18 April 2020 2020 04 18 aged 78 Paris FranceNationalityFrenchAlma materParis Sud UniversityKnown forSzpiro s conjectureAwardsPrix Doistau Blutel 1987 Fellow of the American Mathematical Society 2012 Member of the Academia EuropaeaScientific careerFieldsMathematicsInstitutionsCity University of New YorkCNRSDoctoral advisorPierre SamuelDoctoral studentsAhmed AbbesEmmanuel UllmoShou Wu ZhangInfluencesMaurice AuslanderClaude ChevalleyAlexander Grothendieck Contents 1 Early life and education 2 Career 3 Research 4 Awards 5 Death 6 Selected publications 7 References 8 External linksEarly life and education EditLucien Serge Szpiro was born on 23 December 1941 in the 20th arrondissement of Paris France 1 2 Szpiro attended Paris Sud University where he earned his Ph D under Pierre Samuel 1 3 His doctoral work was heavily influenced by the seminars of Maurice Auslander Claude Chevalley and Alexander Grothendieck 1 He earned his Doctorat d Etat DrE in 1971 1 Career EditFrom 1963 to 1965 Szpiro worked as an assistant high school teacher in Paris 1 4 From 1965 to 1969 he was an assistant professor maitre assistant at the University of Paris 1 4 From 1969 to 1999 Szpiro worked at the CNRS initially as an attache at Paris Diderot University before rising to the rank of a distinguished professor Directeur de Recherche de Classe Exceptionnelle at Paris Sud University 4 In 1999 he became an emeritus professor Directeur de Recherche emerite at the CNRS and moved to the CUNY Graduate Center as a Distinguished Professor 1 4 5 He also held visiting positions at several institutions including Columbia University and the Institute for Advanced Study 4 6 Szpiro was the editor in chief of Asterisque from 1991 to 1993 and an editor of the Bulletin de la Societe Mathematique de France from 1984 to 1990 1 He was also head of the commission that oversaw the Societe mathematique de France libraries 7 Szpiro advised 17 doctoral students including Ahmed Abbes Emmanuel Ullmo and Shou Wu Zhang 1 3 Research EditIn the 1970s Szpiro s research in commutative algebra led to his proof of the Auslander zero divisor conjecture 8 Together with Christian Peskine he developed the liaison theory of algebraic varieties 8 In the 1980s Szpiro s research interests shifted to Diophantine geometry first over function fields and then over number fields 8 The Institut des hautes etudes scientifiques described Szpiro as being the first to realise the importance of a paper by Arakelov for questions of Diophantine geometry which ultimately led to the development of Arakelov theory as a tool of modern Diophantine geometry exemplified by Gerd Faltings s proof of the Mordell conjecture 5 8 Szpiro also showed the link between the positivity of the dualising sheaf of a curve and the Bogomolov conjecture 8 In 1981 Szpiro formulated a conjecture now known as Szpiro s conjecture relating the discriminant of an elliptic curve with its conductor 9 His conjecture inspired the abc conjecture 10 which was later shown to be equivalent to a modified form of Szpiro s conjecture in 1988 11 Szpiro s conjecture and its equivalent forms have been described as the most important unsolved problem in Diophantine analysis by Dorian Goldfeld 12 in part to its large number of consequences in number theory including Roth s theorem the Mordell conjecture the Fermat Catalan conjecture and Brocard s problem 13 14 15 16 After moving to the CUNY Graduate Center in 1999 Szpiro began working on new research in algebraic dynamics 5 8 Awards EditIn 1987 Szpiro received the Prix Doistau Blutel from the French Academy of Sciences for his work in Commutative Algebra and Algebraic Geometry and for his contribution to G Faltings proof of the Mordell conjecture 5 In 2012 he became a fellow of the American Mathematical Society 17 He was a Member of the Academia Europaea 4 Death EditSzpiro died on 18 April 2020 in Paris France from cardiac arrest 18 8 Selected publications EditPesenti Jerome Szpiro Lucien 2000 Inegalite du discriminant pour les pinceaux elliptiques a reductions quelconques Compositio Mathematica 120 1 83 117 doi 10 1023 A 1001736823128 Peskine Christian Szpiro Lucien 1973 Dimension projective finie et cohomologie locale Applications a la demonstration de conjectures de M Auslander H Bass et A Grothendieck Publications Mathematiques de l IHES in French 42 1 47 119 doi 10 1007 BF02685877 ISSN 0073 8301 S2CID 124116905 Peskine Christian Szpiro Lucien 1974 Liaison des varietes algebriques I Inventiones Mathematicae in French 26 4 271 302 Bibcode 1974InMat 26 271P doi 10 1007 BF01425554 ISSN 0020 9910 S2CID 123364655 Szpiro Lucien Ullmo Emmanuel Zhang Shou Wu 1997 Equirepartition des petits points Inventiones Mathematicae in French 127 2 337 347 Bibcode 1997InMat 127 337S doi 10 1007 s002220050123 S2CID 119668209 Szpiro Lucien 1979 Sur le theoreme de rigidite de Parsin et Arakelov Asterisque Journees de geometrie algebrique de Rennes Juillet 1978 II Groupes formels representations galoisiennes et cohomologie des varietes de caracteristique positive 64 169 202 MR 0563470 Szpiro Lucien 1981 Seminaire sur les pinceaux des courbes de genre au moins deux Asterisque 86 3 44 78 Zbl 0463 00009 Szpiro Lucien 1987 Presentation de la theorie d Arakelov In Ribet Kenneth A ed Current Trends in Arithmetical Algebraic Geometry Contemporary Mathematics Vol 67 pp 279 293 doi 10 1090 conm 067 902599 ISBN 9780821850749 Zbl 0634 14012 Szpiro Lucien Conjecture de Mordell Seminaire Nicolas Bourbaki 1983 4 References Edit a b c d e f g h i Curriculum Vitae PDF 2010 Retrieved 19 April 2020 Fichiers des personnes decedees depuis 1970 Fichier des personnes decedees in French a href Template Cite web html title Template Cite web cite web a Missing or empty url help a b Lucien Szpiro at the Mathematics Genealogy Project a b c d e f Lucien Szpiro Academia Europaea Retrieved 18 April 2020 a b c d Lucien Szpiro Graduate Center CUNY Retrieved 18 April 2020 Lucien Szpiro Institute for Advanced Study 9 December 2019 Retrieved 19 April 2020 Un reseau de biblitheques specialisees le reseau des bibliotheques de mathematiques PDF Ecole Nationale Superieure des Sciences de l Information et des Bibliotheques in French 1992 Retrieved 19 April 2020 Lucien Szpiro responsable de la commission des bibliotheques de la SMF estime que le cout de l operation serait de 100 000 francs par an pour un reseau ne contenant que des listes de livres et de preprints a b c d e f g Mathematician Lucien Szpiro passed away at the age of 78 Institut des hautes etudes scientifiques 20 April 2020 Retrieved 21 December 2020 Lang Serge 1997 Survey of Diophantine geometry Berlin Springer Verlag p 51 ISBN 3 540 61223 8 Zbl 0869 11051 Fesenko Ivan 2015 Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions notes on the work of Shinichi Mochizuki PDF European Journal of Mathematics 1 3 405 440 doi 10 1007 s40879 015 0066 0 S2CID 52085917 Oesterle Joseph 1988 Nouvelles approches du theoreme de Fermat Asterisque Seminaire Bourbaki exp 694 161 165 186 ISSN 0303 1179 MR 0992208 Goldfeld Dorian 1996 Beyond the last theorem Math Horizons 4 September 26 34 doi 10 1080 10724117 1996 11974985 JSTOR 25678079 Bombieri Enrico 1994 Roth s theorem and the abc conjecture Preprint ETH Zurich Elkies N D 1991 ABC implies Mordell International Mathematics Research Notices 1991 7 99 109 doi 10 1155 S1073792891000144 Pomerance Carl 2008 Computational Number Theory The Princeton Companion to Mathematics Princeton University Press pp 361 362 Dabrowski Andrzej 1996 On the diophantine equation x A y2 Nieuw Archief voor Wiskunde IV 14 321 324 Zbl 0876 11015 List of Fellows of the American Mathematical Society retrieved 5 August 2013 Lucien Szpiro 1941 2020 Not Even Wrong External links Edit Website at CUNY Lucien Szpiro at the Mathematics Genealogy Project Search on author Lucien Szpiro from Google Scholar Peskine Christian Martin Deschamps Mireille Elkik Renee Goldfeld Dorian Zhang Shouwu Tucker Thomas November 2021 Lucien Szpiro 1941 2020 PDF Notices of the American Mathematical Society 68 10 1763 1777 doi 10 1090 noti2361 Retrieved from https en wikipedia org w index php title Lucien Szpiro amp oldid 1126627987, wikipedia, wiki, book, books, library,

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