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
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 = ...
, 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
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 = ...
from 1975 to 1988. He was a professor of mathematics at
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 ...
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
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.
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
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. Vicente (1977)
* ''Geometric singularity theory'' / editors of the volume, Heisuke Hironaka, Stanisław Janeczko (2004)
See also
*
Hironaka decomposition
*
Hironaka's criterion
*
René Thom
René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958.
He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he becam ...
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