Masa-Hiko SAITO

Masa-Hiko SAITO

Department of Mathematics,
Graduate School of Science, Kobe University
Division : Algebra
Professor		 Building B, Room 214

Personal Website
Research Field : Algebraic Geometry, Geometric approach to Integrable Systems, Moduli theory, Differential Equations of Painlevé type, Mirror symmetry
Research Summary : Algebraic Geometry is a fundamental area of Mathematics and has a long history. I have been working in this research field since 1980. The main research targets in this field are figures defined by algebraic equations, like lines, circles, parabola and curves of degree d in 2-dimensional plane. However, research interests of Algebraic Geometry have been expanded to Complex Geometry, Singularity Theory, Arithmetic Geometry, Cryptography, Mathematical Physics, Integrable Systems and so on. After establishing the basic theory of schemes, cohomology and many other technical developments, Algebraic Geometry can be applied to the many other areas and obtained much flexibility to attack many problems in mathematics, physics and other areas in science and technology. My research interests can be listed up in the following areas: Hodge theory, Kodaira-Spencer deformation theory, Mirror symmetry conjecture, Geometry of Painlevé equations, Moduli theoretic approach for Riemman-Hilbert correspondences.
Primary Publications :
  1. Michi-aki Inaba, Masa-Hiko Saito: Moduli of unramified irregular singular parabolic connections on a smooth projective curve. Kyoto Journal of Mathematics, Vol. 53, No. 2 (2013), 433--482.
  2. Frank Loray, Masa-Hiko Saito and Carlos T. Simpson: Foliations on the moduli space of rank two connections on the projective line minus four points, Séminaires et Congrès 27 (2013), 115--168.
  3. Masa-Hiko Saito: Differential equations of Painlevé type and Algebraic Geometry (JAPANESE), Sugaku 62 (2010), no. 4, 524--544.
  4. Marius van der Put and Masa-Hiko Saito: Moduli spaces for linear differential equations and the Painlevé equations (Espaces de modules pour des équations différentielles liné aires et équations de Painlevé), Annales de l'institut Fourier 59 no. 7 (2009), 2611--2667.
  5. Michi-aki Inaba, Katsunori Iwasaki and Masa-Hiko Saito: Moduli of Stable Parabolic Connections, Riemann-Hilbert correspondence and Geometry of Painlevé equations of type VI, Part II, Advanced Studies in Pure Mathematics 45 (2006), Moduli Spaces and Arithmetic Geometry (Kyoto, 2004), 387--432.
  6. Michi-aki Inaba, Katsunori Iwasaki and Masa-Hiko Saito: Moduli of Stable Parabolic Connections, Riemann-Hilbert correspondence and Geometry of Painlevé equations of type VI, Part I, Publ. Res. Inst. Math. Sci. 42 (2006), no. 4, 987--1089.
  7. Masa-Hiko Saito, Taro Takebe and Hitomi Terajima: Deformation of Okamoto--Painlevé Pairs and Painlevé equations, J. Algebraic Geom. 11 (2002), 311-362.
  8. Shinobu Hosono, Masa-Hiko Saito, and Atsushi Takahashi: Relative Lefschetz action and BPS state counting, Internat. Math. Res. Notices, (2001), No. 15, 783-816.
  9. Shinobu Hosono, Masa-Hiko Saito and Atsushi Takahashi, Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface (Adv. Theor. Math. Phys. 3, (1999), 177--208.