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no. 5
Mathematical works of Hiroshi Umemura
Kazuo Okamoto1 ; Yousuke Ohyama2
1 National Institution for Academic Degrees and Quality Enhancement of Higher Education, 1-29-1 Gakuen-nishimachi Kodaira-shi, Tokyo 187-8587, Japan
2 Department of Mathematical Sciences, Tokushima University, 2-1 Minamijyousanjima-cho, Tokushima 770-8506, Japan
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1053-1062.

Nous donnons un aperçu des recherches mathématiques de Hiroshi Umemura sur la géométrie algébrique, les équations de Painlevé et la théorie de Galois différentielle.

We give an overview of Umemura’s mathematical research on algebraic geometry, the Painlevé equations and the Galois differential theory.

Publié le :
DOI : 10.5802/afst.1656
Kazuo Okamoto 1 ; Yousuke Ohyama 2

1 National Institution for Academic Degrees and Quality Enhancement of Higher Education, 1-29-1 Gakuen-nishimachi Kodaira-shi, Tokyo 187-8587, Japan
2 Department of Mathematical Sciences, Tokushima University, 2-1 Minamijyousanjima-cho, Tokushima 770-8506, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Kazuo Okamoto; Yousuke Ohyama. Mathematical works of Hiroshi Umemura. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1053-1062. doi : 10.5802/afst.1656. https://afst.centre-mersenne.org/articles/10.5802/afst.1656/

[1] Daniel Bertrand; Hiroshi Umemura On the definitions of the Painlevé equations, RIMS Kokyuroku, Volume 1296 (2002), pp. 29-34

[2] Guy Casale The Galois groupoid of Picard-Painlevé VI equation, RIMS Kôkyûroku Bessatsu, Volume B2 (2007), pp. 15-20 | MR | Zbl

[3] Guido Castelnuovo; Federigo Enriques Grundeigenschaften der Algebraischen Flächen, Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Volume 2 (1915) no. 1, pp. 744-755 | Zbl

[4] Jules Drach Essai sur une théorie générale de l’intégration et sur la classification des transcendantes, Ann. Sci. Éc. Norm. Supér. (1898), pp. 243-384 | DOI | Zbl

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[6] Satoshi Fukutani; Kazuo Okamoto; Hiroshi Umemura Special polynomials and the Hirota bilinear relations of the second and the fourth Painlevé equations, Nagoya Math. J., Volume 159 (2000), pp. 179-200 | DOI | Zbl

[7] Florian Heiderich Introduction to the Galois theory of Artinian simple module algebras, Geometric and differential Galois theories (Séminaires et Congrès), Volume 27, Société Mathématique de France, 2013, pp. 69-92 | MR

[8] Bernard Malgrange Le groupoïde de Galois d’un feuilletage, Essays on geometry and related topics (Monographies de l’Enseignement Mathématique), Volume 2, L’Enseignement Mathématique, 2001, pp. 465-501 | Zbl

[9] Akira Masuoka; Katsunori Saito; Hiroshi Umemura Toward quantization of Galois theory, Ann. Fac. Sci. Toulouse, Math., Volume 29 (2020) no. 5, pp. 1319-1431

[10] Shuji Morikawa; Katsunori Saito; Taihei Takeuchi; Hiroshi Umemura Discrete Burgers’ equation, binomial coefficients and mandala, Math. Comput. Sci., Volume 4 (2010) no. 2-3, pp. 151-167 | DOI | MR | Zbl

[11] Shuji Morikawa; Hiroshi Umemura On a general difference Galois theory. II, Ann. Inst. Fourier, Volume 59 (2009) no. 7, pp. 2733-2771 | DOI | Numdam | MR | Zbl

[12] Shigeru Mukai; Hiroshi Umemura Minimal rational threefolds, Algebraic geometry (Tokyo and Kyoto 1982) (Lecture Notes in Mathematics), Volume 1016, Springer, 1983, pp. 490-518 | DOI | MR | Zbl

[13] Keiji Nishioka A note on the transcendency of Painlevé’s first transcendent, Nagoya Math. J., Volume 109 (1988), pp. 63-67 | DOI | MR | Zbl

[14] Masatoshi Noumi; Soichi Okada; Kazuo Okamoto; Hiroshi Umemura Special polynomials associated with the Painlevé equations. II, Integrable systems and algebraic geometry, World Scientific, 1997, pp. 349-372 | Zbl

[15] Paul Painlevé Leçons sur la théorie analytique des équations différentielles, professées à Stockholm (1895), Hermann, 1897 (Oeuvres I, pp. 199–807) | Zbl

[16] Paul Painlevé Analyse des Travaux Scientifiques Jusqu’en 1900, Blanchard, 1900 (Oeuvres I, p. 75–196) | Zbl

[17] Paul Painlevé Sur l’irréductibilité des transcendantes uniformes définies par les équations différentielles du second ordre, C. R. Math. Acad. Sci. Paris, Volume 135 (1902), pp. 411-415 | Zbl

[18] Jean-Francois Pommaret Differential Galois Theory, Mathematics and its Applications, 15, Gordon and Breach Science Publishers, 1983 | MR

[19] Katsunori Saito; Hiroshi Umemura Can we quantize Galois theory?, Proceedings of Various aspects of the Painlevé equations (to appear)

[20] Masa-Hiko Saito; Hiroshi Umemura Painlevé equations and deformations of rational surfaces with rational double points, Physics and combinatorics (Nagoya, 1999), World Scientific, 2001, pp. 320-365 | DOI | Zbl

[21] Hiroshi Umemura Formal moduli for p-divisible groups, Nagoya Math. J., Volume 42 (1971), pp. 1-7 | DOI | MR | Zbl

[22] Hiroshi Umemura Dimension cohomologique des groupes algébriques commutatifs, Ann. Sci. Éc. Norm. Supér., Volume 5 (1972), pp. 265-276 | DOI | Numdam | MR | Zbl

[23] Hiroshi Umemura Fibrés vectoriels positifs sur une courbe elliptique, Bull. Soc. Math. Fr., Volume 100 (1972), pp. 431-433 | DOI | Numdam | MR | Zbl

[24] Hiroshi Umemura La dimension cohomologique des surfaces algébriques, Nagoya Math. J., Volume 47 (1972), pp. 155-160 | DOI | MR | Zbl

[25] Hiroshi Umemura Cohomological dimension of group schemes, Nagoya Math. J., Volume 52 (1973), pp. 47-52 | DOI | MR | Zbl

[26] Hiroshi Umemura Some results in the theory of vector bundles, Nagoya Math. J., Volume 52 (1973), pp. 97-128 | DOI | MR | Zbl

[27] Hiroshi Umemura A theorem of Matsushima, Nagoya Math. J., Volume 54 (1974), pp. 123-134 | DOI | MR | Zbl

[28] Hiroshi Umemura Stable vector bundles with numerically trivial Chern classes over a hyperelliptic surface, Nagoya Math. J., Volume 59 (1975), pp. 107-134 | DOI | MR | Zbl

[29] Hiroshi Umemura On a certain type of vector bundles over an Abelian variety, Nagoya Math. J., Volume 64 (1976), pp. 31-45 | DOI | MR | Zbl

[30] Hiroshi Umemura On a property of symmetric products of a curve of genus 2, Proceedings of the International Symposium on Algebraic Geometry (Kyoto, 1977), Kinokuniya Book-Store, 1977, pp. 709-721 | Zbl

[31] Hiroshi Umemura On a theorem of Ramanan, Nagoya Math. J., Volume 69 (1978), pp. 131-138 | DOI | MR | Zbl

[32] Hiroshi Umemura Moduli spaces of the stable vector bundles over abelian surfaces, Nagoya Math. J., Volume 77 (1980), pp. 47-60 | DOI | MR | Zbl

[33] Hiroshi Umemura Sur les sous-groupes algébriques primitifs du groupe de Cremona à trois variables, Nagoya Math. J., Volume 79 (1980), pp. 47-67 | DOI | MR | Zbl

[34] Hiroshi Umemura Maximal algebraic subgroups of the Cremona group of three variables. Imprimitive algebraic subgroups of exceptional type, Nagoya Math. J., Volume 87 (1982), pp. 59-78 | DOI | MR | Zbl

[35] Hiroshi Umemura On the maximal connected algebraic subgroups of the Cremona group. I, Nagoya Math. J., Volume 88 (1982), pp. 213-246 | DOI | MR | Zbl

[36] Hiroshi Umemura Algebro-geometric problems arising from Painlevé’s works, Algebraic and Topological Theories –to the memory of Dr. Takehiko MIYATA, Kinokuniya Company Ltd, 1984, pp. 467-495 | Zbl

[37] Hiroshi Umemura Resolutions of algebraic equations by theta constants, Tata Lectures on Theta II (Progress in Mathematics), Volume 43, Birkhäuser, 1984 | Zbl

[38] Hiroshi Umemura Birational automorphism groups and differential equations, Équations différentielles dans le champ complexe, Vol. II (Strasbourg, 1985) (Publ. Inst. Rech. Math. Av.), Univ. Louis Pasteur, 1985, pp. 119-227

[39] Hiroshi Umemura Gino Fano, Sūgaku, Volume 37 (1985), pp. 169-178 | MR | Zbl

[40] Hiroshi Umemura On the maximal connected algebraic subgroups of the Cremona group. II, Advanced Studies in Pure Mathematics, 6, North-Holland, 1985 | MR | Zbl

[41] Hiroshi Umemura Minimal rational threefolds. II, Nagoya Math. J., Volume 110 (1988), pp. 15-80 | DOI | MR | Zbl

[42] Hiroshi Umemura On the irreducibility of Painlevé differential equations, Sūgaku, Volume 40 (1988) no. 1, pp. 47-61 translated in Sugaku Expositions, 2 (1989), p. 231–252.

[43] Hiroshi Umemura On the irreducibility of the first differential equation of Painlevé, Algebraic geometry and commutative algebra, Vol. II, Volume 771, Konokuniya Company Ltd, 1988, pp. 771-789 | DOI | Zbl

[44] Hiroshi Umemura On classical numbers, Sūgaku, Volume 41 (1989), pp. 1-15 translated in Sugaku Expositions 4 (1991), p. 1–20 | MR | Zbl

[45] Hiroshi Umemura On the Lie-Drach-Vessiot theory, Proceeding of symposium on algebraic geometry, 1989, pp. 173-198

[46] Hiroshi Umemura Birational automorphism groups and differential equations, Nagoya Math. J., Volume 119 (1990), pp. 1-80 | DOI | MR | Zbl

[47] Hiroshi Umemura Second proof of the irreducibility of the first differential equation of Painlevé, Nagoya Math. J., Volume 117 (1990), pp. 125-171 | DOI

[48] Hiroshi Umemura Classical solutions to Painlevé equations, RIMS Kokyuroku, Volume 857 (1994), pp. 63-80 | Zbl

[49] Hiroshi Umemura On a class of numbers generated by differential equations related with algebraic groups, Nagoya Math. J., Volume 133 (1994), pp. 1-55 | DOI | MR

[50] Hiroshi Umemura The Painlevé equation and classical functions, Sūgaku, Volume 47 (1995), pp. 341-359 translated in Sugaku Expositions 11 (1998), p. 77–100 | Zbl

[51] Hiroshi Umemura Differential Galois theory of infinite dimension, Nagoya Math. J., Volume 144 (1996), pp. 59-135 | DOI | MR | Zbl

[52] Hiroshi Umemura Galois theory of algebraic and differential equations, Nagoya Math. J., Volume 144 (1996), pp. 1-58 | DOI | MR | Zbl

[53] Hiroshi Umemura Special polynomials associated with the Painlevé equations. I, Ann. Fac. Sci. Toulouse, Math., Volume 29 (1996) no. 5, pp. 1063-1089 (talks in Theory of nonlinear special functions: the Painlevé transcendents)

[54] Hiroshi Umemura Lie-Drach-Vessiot theory—infinite-dimensional differential Galois theory, CR-geometry and overdetermined systems (Osaka, 1994) (Advanced Studies in Pure Mathematics), Volume 25, 1997, pp. 364-385 | DOI | MR | Zbl

[55] Hiroshi Umemura 100 years of the Painlevé equation, Sūgaku, Volume 51 (1999), pp. 395-420

[56] Hiroshi Umemura Lie-Drach-Vessiot theory and Painlevé equations, RIMS Kokyuroku, Volume 1150 (2000), pp. 63-69 | Zbl

[57] Hiroshi Umemura On the transformation group of the second Painlevé equation, Nagoya Math. J., Volume 157 (2000), pp. 15-46 | DOI | Zbl

[58] Hiroshi Umemura Theory on elliptic functions, University of Tokyo Press, 2000

[59] Hiroshi Umemura On the definitions of the Painlevé equations, Proceeding of symposium on algebraic geometry, 2002, pp. 76-83

[60] Hiroshi Umemura Monodromy preserving deformation and differential Galois group. I, Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes. I (Astérisque), Volume 296, Société Mathématique de France, 2004, pp. 253-269 | Numdam | Zbl

[61] Hiroshi Umemura Galois theory and Painlevé equations, Théories asymptotiques et équations de Painlevé (Séminaires et Congrès), Volume 14, Société Mathématique de France, 2006, pp. 299-339 | MR | Zbl

[62] Hiroshi Umemura Invitation to Galois theory, Differential equations and quantum groups (IRMA Lectures in Mathematics and Theoretical Physics), Volume 9, European Mathematical Society, 2007, pp. 269-289 | MR | Zbl

[63] Hiroshi Umemura Sur l’équivalence des théories de Galois différentielles générales, C. R. Math. Acad. Sci. Paris, Volume 346 (2008), pp. 1155-1158 | DOI | MR

[64] Hiroshi Umemura On the definition of the Galois groupoid, Differential equations and singularities (Astérisque), Volume 323, 2009, pp. 441-452 | Numdam | MR | Zbl

[65] Hiroshi Umemura Galois: la magnifique théorie de l’ambiguïté, Gendai-Sugakusha, 2011

[66] Hiroshi Umemura Picard-Vessiot theory in general Galois theory, Algebraic methods in dynamical systems (Banach Center Publications), Volume 94, Polish Academy of Sciences, 2011, pp. 263-293 | MR | Zbl

[67] Hiroshi Umemura; Humihiko Watanabe Solutions of the second and fourth Painlevé equations. I, Nagoya Math. J., Volume 148 (1997), pp. 151-198 | DOI | Zbl

[68] Hiroshi Umemura; Humihiko Watanabe Solutions of the third Painlevé equation. I, Nagoya Math. J., Volume 151 (1998), pp. 1-24 | DOI | Zbl

[69] Ernest Vessiot Sur la théorie des groupes continus, Ann. Sci. Éc. Norm. Supér., Volume 20 (1903), pp. 411-451 | DOI | Numdam | MR | Zbl

[70] Ernest Vessiot Sur la théorie de Galois et ses diverses généralisations, Ann. Sci. Éc. Norm. Supér., Volume 21 (1904), pp. 9-85 | DOI | Numdam | MR | Zbl

[71] Ernest Vessiot Sur l’intégration des systèmes différentiels qui admettent des groupes continus de transformations, Acta Math., Volume 28 (1904), pp. 307-349 | DOI | Zbl

[72] Ernest Vessiot Sur une théorie générale de la réductibilité des équations et systèmes d’équations finies ou différentielles, Ann. Sci. Éc. Norm. Supér., Volume 63 (1946), pp. 1-22 | DOI | Numdam | MR | Zbl

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