is a Japanese

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who was awarded the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

in 1970 for his contributions to

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

Career

Hironaka entered

Kyoto University , mottoeng = Freedom of academic culture , established = , type = Public (National) , endowment = ¥ 316 billion (2.4 billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff = 3,978 (Total Staff) , students = ...

in 1949. After completing his undergraduate studies at

, he received his Ph.D. in 1960 from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of highe ...

while under the direction of Oscar Zariski. Hironaka held teaching positions at

Brandeis University , mottoeng = "Truth even unto its innermost parts" , established = , type = Private research university , accreditation = NECHE , president = Ronald D. Liebowitz , p ...

from 1960-1963,

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

in 1964, and

from 1975 to 1988. He was a professor of mathematics at

from 1968 until becoming ''

emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

'' in 1992 and was a president of Yamaguchi University from 1996 to 2002.

Research

In 1964, Hironaka proved that singularities of algebraic varieties admit resolutions in characteristic zero. This means that any

algebraic variety Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. ...

can be replaced by (more precisely is birationally equivalent to) a similar variety which has no singularities. He also introduced

Hironaka's example In geometry, Hironaka's example is a non-Kähler complex manifold that is a deformation of Kähler manifolds found by . Hironaka's example can be used to show that several other plausible statements holding for smooth varieties of dimension at most ...

showing that a deformation of

Kähler manifold In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arn ...

s 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.

Awards

Hironaka was awarded the

in 1970.

Personal life

Hironaka has been active in raising funds for causes such as mathematical education. His wife

Wakako Hironaka is a Japanese writer and politician. She served four terms in the House of Councillors, the upper house of the national Diet, from 1986 until 2010. Her husband is Heisuke Hironaka, a mathematician. Politician Hironaka was first elected to the Ho ...

is a politician. His daughter, Eriko Hironaka, is also a mathematician and focuses on low-dimensional topology and

geometric topology In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originate ...

.https://www.math.fsu.edu/~hironaka/Vita/vita2016.pdf

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

External links

* * * Jackson, Allyn
Interview with Heisuke Hironaka
''Notices of the American Mathematical Society''; vol. 52, no. 9 (October 2005). {{DEFAULTSORT:Hironaka, Heisuke 1931 births 20th-century Japanese mathematicians 21st-century Japanese mathematicians Algebraic geometers Fields Medalists Harvard University alumni Harvard University faculty Brandeis University faculty Columbia University faculty Kyoto University alumni Kyoto University faculty Institute for Advanced Study visiting scholars Living people Members of the French Academy of Sciences Foreign Members of the Russian Academy of Sciences Spouses of Japanese politicians Recipients of the Order of Culture Chevaliers of the Légion d'honneur People from Iwakuni, Yamaguchi