## Shigefumi Mori

Director-General and Distinguished Professor

### Research Fields

Algebraic Geometry, Birational Geometry

### Research Overview

Mori studies three-dimensional (3D) classification problems in a subfield known as birational classification theory of algebraic geometry. Algebraic geometry is a field in science that deals with shapes known as "algebraic varieties." Such an algebraic variety can appear in many slightly different forms if it is of dimension 2 (2D) or higher. The differences between these forms may be understood as partial dents or sharp points similar to those that appear in a physical object when it is struck by another. "Birational classification" refers to an approach where we ignore these minor differences when classifying algebraic varieties. It was known that one could make surfaces into minimal ones and minimize these differences by collapsing certain curves to points. This operation was known as the minimal model program (MMP).

For a long period of time, the generalization of the MMP to dimension three or higher was considered to be difficult; however, the introduction of extremal ray theory and application of general perspectives in [2] was a major trigger for the development of 3D MMP. Following this, MMP was developed, and it was discovered that in a broad sense, 3D birational classification theory is linked to the conjectural existence of an operation known as "flip." Furthermore, in [3], by proving the existence of 3D flips, the problem of 3D MMP was resolved. Hence, the 3D birational classification theory was completed in a rough sense. Subsequently, with the contribution of many researchers, MMPs of dimension four or higher have been established in a practical form.

### Biography

1973 | B.Sc., Faculty of Science, Kyoto University |
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1975 | M.Sc., Graduate School of Science, Kyoto University |

1978 | Ph.D., Kyoto University |

1975-1980 | Assistant of Faculty of Science, Kyoto University |

1980-1982 | Lecturer of Faculty of Science, Nagoya University |

1982-1987 | Associate Professor of Faculty of Science, Nagoya University |

1988-1990 | Professor of Faculty of Science, Nagoya University |

1990-2016 | Professor of Research Institute for Mathematical Sciences, Kyoto University |

2011-2014 | Director of Research Institute for Mathematical Sciences, Kyoto University |

2016- | Director-General and Distinguished Professor of KUIAS |

### Selected Papers

- S. Mori, Projective manifolds with ample tangent bundles,
*Ann. Math.*110, 593–606 (1979). - S. Mori, Threefolds whose canonical bundles are not numerically effective,
*Ann. Math.*116, 133–176 (1982). - S. Mori, Flip theorem and the existence of minimal models for 3-folds,
*J. Amer. Math. Soc.*1, 117–253 (1988). - J. Kollar, S. Mori, Classification of three dimensional flips,
*J. Amer. Math. Soc.*5, 533–703 (1992);*Erratum*20, 269–271 (2007). - S. Mori, Y. Prokhorov, On Q-conic bundles,
*Publ. Res. Inst. Math. Sci.*44, 315–369 (2008).

### Honors

Iyanaga Prize of Mathematical Society of Japan (1983), Autumn Prize of Mathematical Society of Japan (1988), Inoue Prize for Science (1989), Frank Nelson Cole Prize (1990), Japan Academy Prize (1990), Fields Medal (1990), Person of Cultural Merit (1990), Foreign Honorary Member of the American Academy of Arts and Sciences (1992), Member of the Japan Academy (1998), Honorary Doctorate of University of Torino (2002), Fujihara Award (2004), University Professor of Nagoya University (2010), President of the International Mathematical Union (2015-2018), Foreign Member of the Russian Academy of Sciences (2016), Foreign Associate of US National Academy of Sciences (2017), Honorary Doctorate of University of Warwick (2017), Kodaira Kunihiko Prize (2019), Kyoto Prefecture Culture Prize for Outstanding Contribution (2020), Order of Culture (2021), Foreign Member of The Academy of Sciences of Turin (2023)