# Heisuke Hironaka

Heisuke Hironaka (広中 平祐, Hironaka Heisuke, born April 9, 1931) is a Japanese mathematician who was awarded the Fields Medal in 1970 for his contributions to algebraic geometry.[1]

Heisuke Hironaka
BornApril 9, 1931 (age 91)
Yuu-chō, Kuga-Gun, Yamaguchi, Japan
(modern-day Iwakuni, Yamaguchi, Japan)
NationalityJapanese
Alma materKyoto University
Harvard University
AwardsAsahi Prize (1967)
Fields Medal (1970)
Order of Culture (1975)
Legion of Honour (2004)
Scientific career
FieldsMathematics
InstitutionsBrandeis University
Harvard University
Columbia University
Kyoto University
Doctoral studentsDave Bayer
William Haboush
Allen Tannenbaum
Bernard Teissier

## Career

Hironaka entered Kyoto University in 1949. After completing his undergraduate studies at Kyoto University, he received his Ph.D. in 1960 from Harvard University while under the direction of Oscar Zariski.[2][3]

Hironaka held teaching positions at Brandeis University from 1960-1963, Columbia University in 1964, and Kyoto University from 1975 to 1988.[4] He was a professor of mathematics at Harvard University from 1968 until becoming emeritus in 1992 and was a president of Yamaguchi University from 1996 to 2002.[5]

## Research

In 1964, Hironaka proved that singularities of algebraic varieties admit resolutions in characteristic zero.[6] 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.[7] In 2017 he posted to his personal webpage a manuscript that claims to prove the existence of a resolution of singularities in positive characteristic.[8]

## Awards

Hironaka was awarded the Fields Medal in 1970.[9]

## Personal life

Hironaka has been active in raising funds for causes such as mathematical education.[10] His wife Wakako Hironaka is a politician. His daughter, Eriko Hironaka, is also a mathematician and focuses on low-dimensional topology and geometric topology.[11]

## List of books available in English

• Formal functions and formal imbeddings / by Heisuke Hironaka and Hideyuki Matsumura (1967)
• On the characters ${\displaystyle \nu }$  and ${\displaystyle \tau }$  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. ^ "Fields Medallists". Kyoto University. Retrieved March 10, 2014.
2. ^ "Meet the 2011 Centennial Medalists". Harvard Magazine. Retrieved March 10, 2014.
3. ^ "GSAS ALUMNI". Harvard College. Archived from the original on February 12, 2012. Retrieved March 10, 2014.
4. ^ "Professor Emeritus". Research Institute for Mathematical Sciences, Kyoto University. Retrieved March 10, 2014.
5. ^ "Former President of Yamaguchi University". Yamaguchi University. Archived from the original on March 10, 2014. Retrieved March 10, 2014.
6. ^ Hironaka, Heisuke (1964), "Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I", Annals of Mathematics, 79 (1): 109–203, doi:10.2307/1970486, JSTOR 1970486
7. ^ Hironaka, Heisuke (1962), "An example of a non-Kählerian complex-analytic deformation of Kählerian complex structures.", Annals of Mathematics, 75 (1): 190–208, doi:10.2307/1970426, JSTOR 1970426
8. ^ "Resolution of singularities in positive characteristics" (PDF). Harvard University. Retrieved May 17, 2017.
9. ^ "Fields Medallists". Kyoto University. Retrieved March 10, 2014.
10. ^ Jackson, Allyn (October 1, 2005). "Interview with Heisuke Hironaka". Notices of the American Mathematical Society. American Mathematical Society (AMS). 52 (9): 1010–1019. ISSN 0002-9920.
11. ^