Kenkichi Iwasawa
Encyclopedia
Kenkichi Iwasawa was a Japan
ese mathematician
who is known for his influence on algebraic number theory
.
Iwasawa was born in Shinshuku-mura, a town near Kiryū
, in Gunma Prefecture
. He attended elementary school
there, but later moved to Tokyo
to attend Musashi High School.
From 1937 to 1940 Iwasawa studied as an undergraduate at Tokyo University, after which he entered graduate school
at Tokyo University and became an assistant in the Department of Mathematics. In 1945 he was awarded a Doctor of Science degree. However, this same year Iwasawa became sick with pleurisy
, and was unable to return to his position at the university until April 1947. From 1949 to 1955 he worked as Assistant Professor at Tokyo University.
In 1950, Iwasawa was invited to Cambridge, Massachusetts
to give a lecture at the International Congress of Mathematicians
on his method to study Dedekind zeta functions using integration over ideles and duality of adeles; this method was also independently obtained by John Tate
and it is sometimes called Tate's thesis
or the Iwasawa-Tate theory. Iwasawa spent the next two years at Institute for Advanced Study
in Princeton
, and in Spring of 1952 was offered a job at the Massachusetts Institute of Technology
, where he worked until 1967.
From 1967 until his retirement in 1986, Iwasawa served as Professor of Mathematics at Princeton. He returned to Tokyo with his wife in 1987.
Iwasawa is perhaps best known for introducing what is now called Iwasawa theory
, which developed from researches on cyclotomic field
s from the later parts of the 1950s. Before that he worked on Lie group
s and Lie algebra
s, introducing the general Iwasawa decomposition
.
Among Iwasawa's most famous students are Robert F. Coleman
, Ralph Greenberg, Gustave Solomon
, and Larry Washington.
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
who is known for his influence on algebraic number theory
Algebraic number theory
Algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as factorization,...
.
Iwasawa was born in Shinshuku-mura, a town near Kiryū
Kiryu, Gunma
is a city in Gunma, Japan, near the cities of Ōta and Ashikaga. Incorporated on March 1, 1921, Kiryū is considered both a city and part of the Greater Tokyo Metropolitan Area, although it is still widely thought of as a rural area...
, in Gunma Prefecture
Gunma Prefecture
is a prefecture of Japan located in the northwest corner of the Kantō region on Honshu island. Its capital is Maebashi.- History :The remains of a Paleolithic man were found at Iwajuku, Gunma Prefecture, in the early 20th century and there is a public museum there.Japan was without horses until...
. He attended elementary school
Elementary school
An elementary school or primary school is an institution where children receive the first stage of compulsory education known as elementary or primary education. Elementary school is the preferred term in some countries, particularly those in North America, where the terms grade school and grammar...
there, but later moved to Tokyo
Tokyo
, ; officially , is one of the 47 prefectures of Japan. Tokyo is the capital of Japan, the center of the Greater Tokyo Area, and the largest metropolitan area of Japan. It is the seat of the Japanese government and the Imperial Palace, and the home of the Japanese Imperial Family...
to attend Musashi High School.
From 1937 to 1940 Iwasawa studied as an undergraduate at Tokyo University, after which he entered graduate school
Graduate school
A graduate school is a school that awards advanced academic degrees with the general requirement that students must have earned a previous undergraduate degree...
at Tokyo University and became an assistant in the Department of Mathematics. In 1945 he was awarded a Doctor of Science degree. However, this same year Iwasawa became sick with pleurisy
Pleurisy
Pleurisy is an inflammation of the pleura, the lining of the pleural cavity surrounding the lungs. Among other things, infections are the most common cause of pleurisy....
, and was unable to return to his position at the university until April 1947. From 1949 to 1955 he worked as Assistant Professor at Tokyo University.
In 1950, Iwasawa was invited to Cambridge, Massachusetts
Cambridge, Massachusetts
Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...
to give a lecture at the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
on his method to study Dedekind zeta functions using integration over ideles and duality of adeles; this method was also independently obtained by John Tate
John Tate
John Torrence Tate Jr. is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry.-Biography:...
and it is sometimes called Tate's thesis
Tate's thesis
In number theory, Tate's thesis is the thesis of where he reformulated the work of Erich Hecke on L-series in terms of Fourier analysis on adelic groups....
or the Iwasawa-Tate theory. Iwasawa spent the next two years at Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, and in Spring of 1952 was offered a job at the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
, where he worked until 1967.
From 1967 until his retirement in 1986, Iwasawa served as Professor of Mathematics at Princeton. He returned to Tokyo with his wife in 1987.
Iwasawa is perhaps best known for introducing what is now called Iwasawa theory
Iwasawa theory
In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur...
, which developed from researches on cyclotomic field
Cyclotomic field
In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to Q, the field of rational numbers...
s from the later parts of the 1950s. Before that he worked on Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s and Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
s, introducing the general Iwasawa decomposition
Iwasawa decomposition
In mathematics, the Iwasawa decomposition KAN of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix...
.
Among Iwasawa's most famous students are Robert F. Coleman
Robert F. Coleman
Robert F. Coleman is an American mathematician, and professor at the University of California, Berkeley. His primary research area is in number theory, with specific interest in p-adic analysis and arithmetic geometry...
, Ralph Greenberg, Gustave Solomon
Gustave Solomon
Gustave Solomon was a mathematician and engineer who was one of the founders of the algebraic theory of error-correction. He received Ph.D. in Mathematics at MIT in 1956 under direction of Kenkichi Iwasawa....
, and Larry Washington.
List of Books available in English
- Lectures on p-adic L-functions / by Kenkichi Iwasawa (1972)
- Local class field theory / Kenkichi Iwasawa (1986) ISBN 0195040309
- Algebraic functions / Kenkichi Iwasawa ; translated by Goro Kato (1993) ISBN 0821845950