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Jean-Marie Souriau
French mathematician and physicist

Jean-Marie Souriau (3 June 1922, Paris – 15 March 2012, Aix-en-Provence) was a French mathematician. He was one of the pioneers of modern symplectic geometry.

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Education and career

Souriau started studying mathematics in 1942 at École Normale Supérieure in Paris. In 1946 he was a research fellow of CNRS and an engineer at ONERA. His PhD thesis, defended in 1952 under the supervision of Joseph Pérès and André Lichnerowicz, was entitled "Sur la stabilité des avions" (On the stability of planes).4

Between 1952 and 1958 he worked at Institut des Hautes Études in Tunis, and since 1958 he was Professor of Mathematics at the University of Provence in Marseille.5 In 1981 he was awarded the Prix Jaffé of the French Academy of Sciences.6

Research

Souriau contributed to the introduction and the development of many important concepts in symplectic geometry, arising from classical and quantum mechanics.7

In particular, he introduced the notion of moment map,89 gave a classification of the homogeneous symplectic manifolds (now known as the Kirillov–Kostant–Souriau theorem), and investigated the coadjoint action of a Lie group, which led to the first geometric interpretation of spin at a classical level.10 He also suggested a program of geometric quantization11 and developed a more general approach to differentiable manifolds by means of diffeologies.1213

Souriau published more than 50 papers in peer-review scientific journals,14 as well as three monographs, on linear algebra,15 on relativity16 and on geometric mechanics.171819 He supervised 9 PhD students.20

References

  1. "Décès de Jean-Marie Souriau" (in French). Société Mathématique de France. Archived from the original on 5 May 2012. Retrieved 19 March 2012. https://web.archive.org/web/20120505062547/http://smf.emath.fr/content/deces-de-jean-marie-souriau ↩

  2. "Décès Jean-Marie Souriau | Société Mathématique de France". smf.emath.fr. Retrieved 2022-02-05. https://smf.emath.fr/node/123126 ↩

  3. Marle, Charles-Michel; de Saxcé, Géry; Vallée, Claude (2012). "Hommage à Jean-Marie Souriau" (PDF). Gazette des Mathématiciens (in French). 133. Société Mathématique de France. https://marle.perso.math.cnrs.fr/publications/HommageSouriaucorrige9.pdf ↩

  4. "Jean-Marie Souriau - The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 2022-01-17. https://www.genealogy.math.ndsu.nodak.edu/id.php?id=112757 ↩

  5. Marle, Charles-Michel; de Saxcé, Géry; Vallée, Claude (2012). "Hommage à Jean-Marie Souriau" (PDF). Gazette des Mathématiciens (in French). 133. Société Mathématique de France. https://marle.perso.math.cnrs.fr/publications/HommageSouriaucorrige9.pdf ↩

  6. "Prix Jaffé" (PDF). academie-sciences.fr (in French). Académie des Sciences. Retrieved 21 January 2022. https://www.academie-sciences.fr/archivage_site/activite/prix/laureat_jaffe.pdf ↩

  7. Bacry, Henri; Ruegg, Henri; Souriau, Jean-Marie (1966-10-01). "Dynamical groups and spherical potentials in Classical Mechanics". Communications in Mathematical Physics. 3 (5): 323–333. Bibcode:1966CMaPh...3..323B. doi:10.1007/BF01645086. ISSN 1432-0916. S2CID 56363683. https://doi.org/10.1007/BF01645086 ↩

  8. Souriau, J.-M. (1970). Structure des systèmes dynamiques: maîtrises de mathématiques (in French). Paris: Dunod. ISBN 2-04-010752-5. OCLC 1041884. 2-04-010752-5 ↩

  9. Souriau, Jean-Marie (2008). Structure des systèmes dynamiques : Maîtrises de mathématiques (in French). Paris: J. Gabay. ISBN 978-2-87647-321-8. OCLC 494510763. 978-2-87647-321-8 ↩

  10. Souriau, Jean-Marie (1974). "Modèle de particule à spin dans le champ électromagnétique et gravitationnel". Annales de l'Institut Henri Poincaré A (in French). 20 (4): 315–364 – via NUMDAM [fr]. http://www.numdam.org/item/?id=AIHPA_1974__20_4_315_0 ↩

  11. Souriau, J.-M. (1966). "Quantification géométrique". Communications in Mathematical Physics. 1 (5): 374–398. ISSN 0010-3616 – via Project Euclid. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-1/issue-5/Quantification-g%c3%a9om%c3%a9trique/cmp/1103758996.full ↩

  12. Souriau, J. M. (1980), García, P. L.; Pérez-Rendón, A.; Souriau, J. M. (eds.), "Groupes differentiels", Differential Geometrical Methods in Mathematical Physics, Lecture Notes in Mathematics, vol. 836, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 91–128, doi:10.1007/bfb0089728, ISBN 978-3-540-10275-5, retrieved 2022-01-17 978-3-540-10275-5 ↩

  13. Souriau, Jean-Marie (1984), Denardo, G.; Ghirardi, G.; Weber, T. (eds.), "Groupes différentiels et physique mathématique", Group Theoretical Methods in Physics, Lecture Notes in Physics, vol. 201, Berlin/Heidelberg: Springer-Verlag, pp. 511–513, doi:10.1007/bfb0016198, ISBN 978-3-540-13335-3, retrieved 2022-01-17 978-3-540-13335-3 ↩

  14. "zbMATH Open - the first resource for mathematics". zbmath.org. Retrieved 2022-01-17. https://zbmath.org/authors/?q=ai:souriau.jean-marie ↩

  15. Souriau, J.-M. (1964). Calcul linéaire : contient la solution détaillée des exercices (in French). Sceaux: Ed. J. Gabay. ISBN 2-87647-097-7. OCLC 27757494. 2-87647-097-7 ↩

  16. Souriau, Jean-Marie (1964). Géométrie et relativité (in French). Paris: J. Gabay. ISBN 978-2-87647-318-8. OCLC 494510220. 978-2-87647-318-8 ↩

  17. Souriau, J.-M. (1970). Structure des systèmes dynamiques: maîtrises de mathématiques (in French). Paris: Dunod. ISBN 2-04-010752-5. OCLC 1041884. 2-04-010752-5 ↩

  18. Souriau, Jean-Marie (2008). Structure des systèmes dynamiques : Maîtrises de mathématiques (in French). Paris: J. Gabay. ISBN 978-2-87647-321-8. OCLC 494510763. 978-2-87647-321-8 ↩

  19. Souriau, Jean-Marie (1997). Structure of Dynamical Systems. Springer Verlag. https://link.springer.com/book/9780817636951 ↩

  20. "Jean-Marie Souriau - The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 2022-01-17. https://www.genealogy.math.ndsu.nodak.edu/id.php?id=112757 ↩