mathematics

Lucien Szpiro

Lucien Szpiro is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Lucien Szpiro rather than just read about it. In short: Lucien 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 at the French National Centre for Scientific Research.

Key takeaways

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Reference excerpt

Lucien 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 at the French National Centre for Scientific Research.

Early life and education Lucien Szpiro was born on 23 December 1941 in Paris, France. Szpiro attended Paris-Sud University where he earned his Doctor of Philosophy under Pierre Samuel. His doctoral work was heavily influenced by the seminars of Maurice Auslander, Claude Chevalley, and Alexander Grothendieck. He earned his Doctorat d'État (DrE) in 1971.

Career From 1963 to 1965, Szpiro worked as an assistant high school teacher in Paris. From 1965 to 1969, he was an assistant professor (maître assistant) at the University of Paris. 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. 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. He also held visiting positions at several institutions including Columbia University and the Institute for Advanced Study. 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. He was also head of the commission that oversaw the Société mathématique de France libraries. Szpiro advised 17 doctoral students, including Ahmed Abbes, Emmanuel Ullmo, and Shou-Wu Zhang.

Research In the 1970s, Szpiro's research in commutative algebra led to his proof of the Auslander zero divisor conjecture. Together with Christian Peskine, he developed the liaison theory of algebraic varieties. In the 1980s, Szpiro's research interests shifted to Diophantine geometry, first over function fields and then over number fields. 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. Szpiro also showed the link between the positivity of the dualising sheaf of a curve and the Bogomolov conjecture. In 1981, Szpiro formulated a conjecture (now known as Szpiro's conjecture) relating the discriminant of an elliptic curve with its conductor. His conjecture inspired the abc conjecture, which was later shown to be equivalent to a modified form of Szpiro's conjecture in 1988. Szpiro's conjecture and its equivalent forms have been described as "the most important unsolved problem in Diophantine analysis" by Dorian Goldfeld, 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. After moving to the CUNY Graduate Center in 1999, Szpiro began working on new research in arithmetic dynamics.

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." In 2012 he became a fellow of the American Mathematical Society. He was a Member of the Academia Europaea.

Death Szpiro died on 18 April 2020 in Paris, France, from cardiac arrest.

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

External links "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.

Illustrations

Worked examples

Example 1 — a first encounter with Lucien Szpiro

Start with the simplest possible case. Write down what Lucien Szpiro claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lucien Szpiro before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lucien Szpiro ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lucien Szpiro

In research: Lucien Szpiro appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lucien Szpiro in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lucien Szpiro is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1941 births, 2020 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lucien Szpiro outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Lucien Szpiro in 20 minutes

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Frequently asked questions

What is Lucien Szpiro in simple terms?

Why does Lucien Szpiro matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lucien Szpiro?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lucien Szpiro.