was a Japanese mathematician known for founding the fields of
algebraic analysis,
hyperfunctions, and holonomic quantum fields. He was a professor at the
Research Institute for Mathematical Sciences
The is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. RIMS was founded in April 1963.
List of directors
* Masuo Fukuhara (1963.5.1 – 1969.3.31)
* Kōsaku Yosida (1969 ...
in Kyoto.
Biography
Born in Tokyo on 18 April 1928,
Sato studied at the
University of Tokyo
The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...
, receiving his BSc in 1952 and PhD under
Shokichi Iyanaga in 1963.
He was a professor at
Osaka University and the
University of Tokyo
The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...
before moving to the
Research Institute for Mathematical Sciences
The is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. RIMS was founded in April 1963.
List of directors
* Masuo Fukuhara (1963.5.1 – 1969.3.31)
* Kōsaku Yosida (1969 ...
(RIMS) attached to
Kyoto University
, or , is a National university, national research university in Kyoto, Japan. Founded in 1897, it is one of the former Imperial Universities and the second oldest university in Japan.
The university has ten undergraduate faculties, eighteen gra ...
in 1970.
He was director of RIMS from 1987 to 1991.
His disciples include
Masaki Kashiwara,
Takahiro Kawai,
Tetsuji Miwa, as well as
Michio Jimbo, who have been called the "Sato School".
Sato died at home in
Kyoto
Kyoto ( or ; Japanese language, Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in the Kansai region of Japan's largest and most populous island of Honshu. , the city had a population of 1.46 million, making it t ...
on 9 January 2023, aged 94.
[
]
Research
Sato was known for his innovative work in a number of fields, such as prehomogeneous vector spaces and Bernstein–Sato polynomials; and particularly for his hyperfunction theory. This theory initially appeared as an extension of the ideas of distribution theory; it was soon connected to the local cohomology theory of Grothendieck, for which it was an independent realisation in terms of sheaf theory. Further, it led to the theory of microfunctions and microlocal analysis in linear partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s and Fourier theory, such as for wave fronts, and ultimately to the current developments in ''D''-module theory. Part of Sato's hyperfunction theory is the modern theory of holonomic systems: PDEs overdetermined to the point of having finite-dimensional spaces of solutions ( algebraic analysis).
In theoretical physics, Sato wrote a series of papers in the 1970s with Michio Jimbo and Tetsuji Miwa that developed the theory of holonomic quantum fields. When Sato was awarded the 2002–2003 Wolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...
, this work was described as "a far-reaching extension of the mathematical formalism underlying the two-dimensional Ising model, and introduced along the way the famous tau functions." Sato also contributed basic work to non-linear soliton
In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is , in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such local ...
theory, with the use of Grassmannian
In mathematics, the Grassmannian \mathbf_k(V) (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all k-dimension (vector space), dimensional linear subspaces of an n-dimensional vector space V over a ...
s of infinite dimension.
In number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
, he and John Tate independently posed the Sato–Tate conjecture on ''L''-functions around 1960.[It is mentioned in J. Tate, ''Algebraic cycles and poles of zeta functions'' in the volume (O. F. G. Schilling, editor), ''Arithmetical Algebraic Geometry'', pages 93–110 (1965).]
Pierre Schapira remarked, "Looking back, 40 years later, we realize that Sato's approach to mathematics is not so different from that of Grothendieck, that Sato did have the incredible temerity to treat analysis
Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
as algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
and was also able to build the algebraic and geometric tools adapted to his problems."
Awards and honours
Sato received the 1969 Asahi Prize of Science, the 1976 Japan Academy Prize, the 1984 Person of Cultural Merits award of the Japanese Education Ministry, the 1997 Schock Prize, and the 2002–2003 Wolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...
.
Sato was a plenary speaker at the 1983 International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before ...
in Warsaw
Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...
. He was elected a foreign member of the National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
in 1993.
Notes
External links
Schock Prize citation
1990 Interview
in the '' AMS Notices''
Mikio Sato, a Visionary of Mathematics
by Pierre Schapira
AMS Notices, (May 2024)
{{DEFAULTSORT:Sato, Mikio
1928 births
2023 deaths
20th-century Japanese mathematicians
21st-century Japanese mathematicians
Foreign associates of the National Academy of Sciences
Academic staff of Kyoto University
Academic staff of Osaka University
Persons of Cultural Merit
Rolf Schock Prize laureates
Scientists from Tokyo
University of Tokyo alumni
Academic staff of the University of Tokyo
Wolf Prize in Mathematics laureates