Lucien Szpiro

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Lucien Serge Szpiro
LucienSzpiro.jpg
Szpiro at the Mathematical Research Institute of Oberwolfach
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

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  [fr] at the CNRS.

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 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[]

References[]

  1. ^ Jump up to: 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). Missing or empty |url= (help)
  3. ^ Jump up to: a b Lucien Szpiro at the Mathematics Genealogy Project
  4. ^ Jump up to: a b c d e f "Lucien Szpiro". Academia Europaea. Retrieved 18 April 2020.
  5. ^ Jump up to: a b c d "Lucien Szpiro". Graduate Center, CUNY. Retrieved 18 April 2020.
  6. ^ "Lucien Szpiro". Institute for Advanced Study. 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. ^ Jump up to: 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[]

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