# Heisuke Hironaka

Heisuke Hironaka
Born April 9, 1931 (age 90)
Yuu-chō, Kuga-Gun, Yamaguchi, Japan
(modern-day Iwakuni, Yamaguchi, Japan)
Nationality Japanese
Fields Mathematics
Institutions Brandeis University
Harvard University
Columbia University
Kyoto University
Alma mater Kyoto University,Harvard University
Doctoral students William Haboush
Allen Tannenbaum
Bernard Teissier
Dave Bayer
Notable awards Asahi Prize (1967)
Fields Medal (1970)
Order of Culture (1975)
Legion of Honour (2004)

Heisuke Hironaka (広中 平祐 Hironaka Heisuke?, born April 9, 1931) is a Japanese mathematician. He entered Kyoto University in 1949. After completing his undergraduate studies at Kyoto University, he received his Ph.D. in 1960 from Harvard while under the direction of Oscar Zariski.[1][2] He was awarded the Fields Medal in 1970.[3]

He is celebrated for proving in 1964 that singularities of algebraic varieties admit resolutions in characteristic zero. This means that any algebraic variety can be replaced by (more precisely is birationally equivalent to) a similar variety which has no singularities. He also introduced Hironaka's example showing that a deformation of Kähler manifolds need not be Kähler.

Hironaka was for many years a Professor of mathematics at Harvard University (1968-1992) but currently lives in Japan. He held teaching positions at Brandeis University (1960-1963), Columbia University (1964) and Kyoto University (1975-1988).[4] He was a president of Yamaguchi University (1996-2002).[5] He has been active in raising funds for causes such as mathematical education.

## Story

Hironaka spoke about the singularity problem of algebraic varieties at the Mathematical Society of Japan. He proposed that he attempts to form a first studies with a variety of restriction conditions than generally think because there is too difficult problem. At that time, Kiyoshi Oka rises, he said"To solve the problem, instead of going with the limit as Hironaka proposed,you should solve by setting a difficult problem that is more idealized conversely rather. Then, Hironaka solved in the idealized form by removing the restriction,It became the winning performance of the Fields Medal.

## List of books available in English

• Formal functions and formal imbeddings / by Heisuke Hironaka and Hideyuki Matsumura (1967)
• On the characters $\nu$ and $\tau$ of singularities / by Heisuke Hironaka
• Introduction to the theory of infinitely near singular points / Heisuke Hironaka (1974)
• The theory of the maximal contact / José M. Aroca, Heisuke Hironaka and José L. Vicente (1975)
• Desingularization theorems / Jose M. Aroca, Heisuke Hironaka and Jose L. Vicente (1977)
• Geometric singularity theory / editors of the volume, Heisuke Hironaka, Stanisław Janeczko (2004)

## References

1. "Meet the 2011 Centennial Medalists". Harvard Magazine. Retrieved March 10, 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
2. "GSAS ALUMNI". Harvard College. Retrieved March 10, 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
3. "Fields Medallists". Kyoto University. Retrieved March 10, 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
4. "Professor Emeritus". Research Institute for Mathematical Sciences, Kyoto University. Retrieved March 10, 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
5. "Former President of Yamaguchi University". Yamaguchi University. Retrieved March 10, 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>