Shigefumi Mori is a mathematician recognized for his work on algebraic geometry. He is known particularly for his theory of extremal rays in higher dimensional birational geometry that works as an important marker for a geometric structure of an algebraic variety. It is a basis for various classification theory of algebraic varieties and the so-called Minimal Model Program, which intends to transform an algebraic variety into one with a simpler global structure and essentially reduce the study of an algebraic variety to those of two simpler opposite classes called minimal models and Fano varieties. Mori was born in Nagoya City, Japan. He obtained B. Sc. in 1973 and D. Sc. in 1978 both from Kyoto University, Japan. He served as Assistant at Kyoto University, Lecturer and Professor at Nagoya University, Professor at Research Institute for Mathematical Sciences of Kyoto University, and since 2016 he has been Distinguished Professor and Director-General of Kyoto University Institute for Advanced Study. He also stayed at several institutions including Harvard University, Institute for Advanced Study Princeton, Columbia University, and University of Utah. He has been President of International Mathematical Union since 2015.

Research Interests

Shigefumi Mori started working in algebraic geometry especially from the viewpoint of how a manifold is curved globally around 1980. His first remarkable work called "Bend-and-Break" in this direction was the existence of a rational curve on a manifold under a mild positive curvature hypothesis, which he applied to settle conjectures characterizing projective spaces in terms of global positive curvature conditions. As a further generalization he created the theory of extremal rays, which brought a new curvature viewpoint to the Hironaka-Kleiman cone of curves. It initiated the so-called Minimal Model Program which intends to transform an algebraic variety into a minimal model, i.e. a weakly non-positively curved one, or a Fano fiber space, i.e. a fiber space which is weakly positively curved over the base, in oversimplified terms. He completed the three dimensional case of the program by proving its last missing step. It was the starting point of the Minimal Model Program currently available in many cases in all dimensions, which is now a fundamental tool to study algebraic varieties.

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International Member

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Section 11: Mathematics