### Shigefumi Mori

Born 23 February 1951, Nagoya, Japan

Fields Medal (1990) “for the proof of Hartshorne’s conjecture and his work on the classification of three-dimensional algebraic varieties.”

Shigefumi Mori’s parents were running a small company dealing in textiles. He attended Kyoto University, taking his Bachelor’s degree in Mathematics in 1973 and a Master’s in 1975. In the same year he became an assistant at the Department, and completed his doctorate under the supervision of Masayoshi Nagata (Ph.D. 1978). The title of his thesis was ‘The endomorphism rings of some abelian varieties’. After receiving his Ph.D. Mori remained at Kyoto University as a research assistant until 1980. He then became a lecturer in Mathematics at Kyoto University. In 1982 he was promoted to Associate Professor, and to Full Professor in 1988. In 1990 Mori became a professor in the Research Institute of Mathematical Sciences (RIMS) at Kyoto University, where he continues to work today. Despite his continuous employment in Japan, Shigefumi Mori spent a lot of time in the United States during the years 1977-1987. He was an Assistant Professor at Harvard University (1977-1980), a Fellow at the Institute for Advanced Study at Princeton (1981-82), and a Visiting Professor at Columbia University (1985-87) and the University of Utah (1987 and 1991-92). He is married, with four children.

In addition to the Fields Medal, Shigefumi Mori has received numerous awards and prizes: in 1983 the Iyanaga Prize from the Mathematical Society of Japan, 1984 the Chunichi Cultural Prize, 1988 the Autumn Prize of the Mathematical Society of Japan (with Yujiro Kawamata), 1989 the Inoue Prize for Science, 1990 the Cole Prize of the American Mathematical Society and in the same year the Japan Academy Prize (with Shigeru Iitaka and Yujiro Kawamata) and the Person of Cultural Merit of the Japanese Government, and 2004 Fujihara award from the Fujihara Foundation of Science; in 1992 he became a Foreign Honorary Member of American Academy of Arts and Science, and in 1999 a Member of the Japan Academy.

Shigefumi Mori works in algebraic geometry. This area of mathematics is concerned with roots of polynomial equations, which are defined by polynomials as one learns at school. These zero sets are called algebraic varieties (or manifolds), and it is their structure that is studied in algebraic geometry.

Mori’s work covers precisely this area, and he has achieved significant results in the classification of algebraic varieties. He also initiated the minimal model program (also called Mori’s program) for a classification of algebraic 3-manifolds using new methods.

In 1978 he became famous by proving the Hartshorne conjecture, formulated eight years earlier by Robin Hartshorne (* 1938). Hartshorne had suspected that the projective space – i. e. the totality of lines in a vector space that pass through the origin – is the only variety with ample tangent bundle. Mori’s proof of this conjecture confirmed that these specific varieties can be characterised simply. A few years later, he completed with Shigeru Mukai the classification of another special class of varieties, Fano 3-folds. In the years that followed, Mori and others were able to complete the minimal model program, which is considered the greatest success of algebraic geometry of the 1980s.