Shigefumi Mori

Shigefumi Mori
Shigefumi Mori
Born	(1951-02-23) February 23, 1951 Nagoya, Japan
Nationality	Japanese
Alma mater	Kyoto University
Known for	Algebraic geometry minimal model program
Awards	Fields Medal (1990) Cole Prize (1990)
Scientific career
Fields	Mathematician
Institutions	Kyoto University
Thesis	The Endomorphism Rings of Some Abelian Varieties  (1978)
Doctoral advisor	Masayoshi Nagata

Shigefumi Mori (森 重文, Mori Shigefumi, born February 23, 1951) is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds.

Career

Mori completed his Ph.D. titled "The Endomorphism Rings of Some Abelian Varieties" under Masayoshi Nagata at Kyoto University in 1978. He was visiting professor at Harvard University during 1977–1980, the Institute for Advanced Study in 1981–82, Columbia University 1985–87 and the University of Utah for periods during 1987–89 and again during 1991–92. He has been a professor at Kyoto University since 1990.

Work

He generalized the classical approach to the classification of algebraic surfaces to the classification of algebraic three-folds. The classical approach used the concept of minimal models of algebraic surfaces. He found that the concept of minimal models can be applied to three-folds as well if we allow some singularities on them. The extension of Mori's results to dimensions higher than three is called the minimal model program and is an active area of research in algebraic geometry.

He has been elected president of the International Mathematical Union, becoming the first head of the group from East Asia.

Awards

He was awarded the Fields Medal in 1990 at the International Congress of Mathematicians.

Major publications

• Mori, Shigefumi. Projective manifolds with ample tangent bundles. Ann. of Math. (2) 110 (1979), no. 3, 593–606.
• Mori, Shigefumi; Mukai, Shigeru. Classification of Fano 3-folds with B₂≥2. Manuscripta Math. 36 (1981/82), no. 2, 147–162.
• Mori, Shigefumi. Threefolds whose canonical bundles are not numerically effective. Ann. of Math. (2) 116 (1982), no. 1, 133–176.
• Mori, Shigefumi. Flip theorem and the existence of minimal models for 3-folds. J. Amer. Math. Soc. 1 (1988), no. 1, 117–253.
• Kollár, János; Miyaoka, Yoichi; Mori, Shigefumi. Rationally connected varieties. J. Algebraic Geom. 1 (1992), no. 3, 429–448.
• Kollár, János; Miyaoka, Yoichi; Mori, Shigefumi. Rational connectedness and boundedness of Fano manifolds. J. Differential Geom. 36 (1992), no. 3, 765–779.
• Kollár, János; Mori, Shigefumi. Classification of three-dimensional flips. J. Amer. Math. Soc. 5 (1992), no. 3, 533–703.
• Keel, Seán; Mori, Shigefumi. Quotients by groupoids. Ann. of Math. (2) 145 (1997), no. 1, 193–213.
• Kollár, János; Mori, Shigefumi. Birational geometry of algebraic varieties. With the collaboration of C. H. Clemens and A. Corti. Translated from the 1998 Japanese original. Cambridge Tracts in Mathematics, 134. Cambridge University Press, Cambridge, 1998. viii+254 pp. ISBN 0-521-63277-3

See also

• Keel–Mori theorem

References

• O'Connor, John J.; Robertson, Edmund F., "Shigefumi Mori", MacTutor History of Mathematics Archive, University of St Andrews
• Heisuke Hironaka, The work of Shigefumi Mori. Fields Medallists Lectures, Michael F. Atiyah (Editor), Daniel Iagolnitzer (Editor); World Scientific Publishing, 2007. ISBN 981-02-3117-2