Toshiki Mabuchi

Toshiki Mabuchi (kanji: 満渕俊樹, hiragana: マブチ トシキ, Mabuchi Toshiki, born in 1950) is a Japanese mathematician, specializing in complex differential geometry and algebraic geometry.[1] In 2006 in Madrid he was an invited speaker at the International Congress of Mathematicians.[2]

Education and career

In 1972 Mabuchi graduated from the University of Tokyo Faculty of Science[1] and became a graduate student in mathematics at the University of California, Berkeley.[3] There he graduated with a Ph.D. in 1977 with thesis C3-Actions and Algebraic Threefolds with Ample Tangent Bundle and advisor Shoshichi Kobayashi[4] As a postdoc Mabuchi was from 1977 to 1978 a guest researcher at the University of Bonn. Since 1978 he is a faculty member of the Department of Mathematics of Osaka University. His research deals with complex differential geometry, extremal Kähler metrics, stability of algebraic varieties, and the Hitchin–Kobayashi correspondence.[1]

In 2006 Toshiki Mabuchi and Takashi Shioya received the Geometry Prize of the Mathematical Society of Japan.

Selected publications

Articles
  • Mabuchi, Toshiki (1987). "Some symplectic geometry on compact Kähler manifolds. I". Osaka journal of mathematics. 24 (2): 227–252.
  • —— (1987). "Einstein-Kähler forms, Futaki invariants and convex geometry on toric Fano varieties". Osaka J. Math. 24 (4): 705–737.
  • Bando, Shigetoshi; —— (1987). "Uniqueness of Einstein Kähler Metrics Modulo Connected Group Actions": 11–40. doi:10.2969/aspm/01010011. ISSN 0920-1971. Cite journal requires |journal= (help)
  • —— (1986). "-energy maps integrating Futaki invariants". Tohoku Mathematical Journal. 38 (4): 575–593. doi:10.2748/tmj/1178228410. ISSN 0040-8735.
  • Hwang, Andrew D.; —— (1993). "A conjecture on the group of biholomorphisms of a nonsingular Fano variety". Internat. J. Math. 4: 833–839.
  • —— (1993). "Q-rationality of moment maps". Proceedings of the Japan Academy, Series A, Mathematical Sciences. 69 (10): 392–394. doi:10.3792/pjaa.69.392. ISSN 0386-2194.
  • Imayoshi, Yoichi; —— (1994). "A Torelli-type theorem for stable curves": 75–95. doi:10.1142/9789814350112_0005. Cite journal requires |journal= (help)
  • Futaki, Akito; —— (1995). "Bilinear forms and extremal Kähler vector fields associated with Kähler classes". Mathematische Annalen. 301 (1): 199–210. doi:10.1007/BF01446626. ISSN 0025-5831.
  • Futaki, Akito; —— (2002). "Moment maps and symmetric multilinear forms associated with symplectic classes" (PDF). Asian Journal of Mathematics. 6 (2): 349–372.

Books
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References
  1. "Mabuchi Toshiki". J-Global - Japan Science and Technology Agency.
  2. Mabuchi, Toshiki (2006). "Extremal metrics and stabilities on polarized manifolds". arXiv preprint math/0603493. (published in vol. 2 of the Proceedings of the ICM, Madrid 2006, pages 813–826)
  3. Mabuchi, Toshiki (July 25, 2013). "Remembering Professor Shoshichi Kobayashi". (translated form the original Japanese by Hisashi Kobayashi)
  4. Toshiki Mabuchi at the Mathematics Genealogy Project
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