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Concept
Heisuke Hironaka
Summary
is a Japanese mathematician who was awarded the Fields Medal in 1970 for his contributions to algebraic geometry.
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.
Hironaka held teaching positions at Brandeis University from 1960-1963, Columbia University in 1964, and Kyoto University from 1975 to 1988. 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.
In 1964, Hironaka proved 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. In 2017 he posted to his personal webpage a manuscript that claims to prove the existence of a resolution of singularities in positive characteristic.
Hironaka was awarded the Fields Medal in 1970.
Hironaka has been active in raising funds for causes such as mathematical education. His wife Wakako Hironaka is a politician. His daughter, Eriko Hironaka, is also a mathematician and focuses on low-dimensional topology and geometric topology.
Formal functions and formal imbeddings / by Heisuke Hironaka and Hideyuki Matsumura (1967)
On the characters and 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.
Official source
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