is a Japanese mathematician known for founding the fields of

algebraic analysis Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctio ...

hyperfunction In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato ...

s, and holonomic quantum fields. He is 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 (196 ...

in Kyoto.

Education

Sato studied at the

University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

and then did graduate study in

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

as a student of Shin'ichiro Tomonaga. Since 1970, Sato has been professor at the

attached to

Kyoto University , mottoeng = Freedom of academic culture , established = , type = National university, Public (National) , endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff ...

. His disciples include

Masaki Kashiwara is a Japanese mathematician. He was a student of Mikio Sato at the University of Tokyo. Kashiwara made leading contributions towards algebraic analysis, microlocal analysis, D-module, ''D''-module theory, Hodge theory, sheaf theory and represent ...

, Takahiro Kawai,

Tetsuji Miwa Tetsuji Miwa (三輪哲二, ''Miwa Tetsuji''; born 10 February 1949 in Tokyo) is a Japanese mathematician, specializing in mathematical physics. Miwa received his undergraduate degree in 1971 and his master's degree in 1973 from the University o ...

, and

Michio Jimbo is a Japanese mathematician working in mathematical physics and is a professor of mathematics at Rikkyo University. He is a grandson of the linguist . Career After graduating from the University of Tokyo in 1974, he studied under Mikio Sato at t ...

, who have been called the "Sato School".

Research

Sato is known for his innovative work in a number of fields, such as

prehomogeneous vector space In mathematics, a prehomogeneous vector space (PVS) is a finite-dimensional vector space ''V'' together with a subgroup ''G'' of the general linear group GL(''V'') such that ''G'' has an open dense orbit in ''V''. Prehomogeneous vector spaces were i ...

s and

Bernstein–Sato polynomial In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by and , . It is also known as the b-function, the b-polynomial, and the Bernstein polynomial, though it is not related ...

s; and particularly for his hyperfunction theory. This theory initially appeared as an extension of the ideas of

distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations * Probability distribution, the probability of a particular value or value range of a vari ...

theory; it was soon connected to the

local cohomology In algebraic geometry, local cohomology is an algebraic analogue of relative cohomology. Alexander Grothendieck introduced it in seminars in Harvard in 1961 written up by , and in 1961-2 at IHES written up as SGA2 - , republished as . Given a fu ...

theory of Grothendieck, for which it was an independent realization in terms of

sheaf Sheaf may refer to: * Sheaf (agriculture), a bundle of harvested cereal stems * Sheaf (mathematics), a mathematical tool * Sheaf toss, a Scottish sport * River Sheaf, a tributary of River Don in England * ''The Sheaf'', a student-run newspaper se ...

theory. Further, it led to the theory of

microfunction Algebraic analysis is an area of mathematics that deals with systems of Partial differential equation, linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of Function (mathematic ...

s and

microlocal analysis In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes genera ...

in linear

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s and

Fourier theory Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an ...

, 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 system In classical mechanics, holonomic constraints are relations between the position variables (and possibly time) that can be expressed in the following form: :f(u_1, u_2, u_3,\ldots, u_n, t) = 0 where \ are the ''n'' generalized coordinates that d ...

s: PDEs overdetermined to the point of having finite-dimensional spaces of solutions (

). He also contributed basic work to non-linear

soliton In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium ...

theory, with the use of

Grassmannian In mathematics, the Grassmannian is a space that parameterizes all -Dimension, dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the ...

s of infinite dimension. In

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

, he and

John Tate John Tate may refer to: * John Tate (mathematician) (1925–2019), American mathematician * John Torrence Tate Sr. (1889–1950), American physicist * John Tate (Australian politician) (1895–1977) * John Tate (actor) (1915–1979), Australian act ...

independently posed the

Sato–Tate conjecture In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves ''Ep'' obtained from an elliptic curve ''E'' over the rational numbers by reduction modulo almost all prime numbers ''p''. Mikio Sato and J ...

on ''L''-functions around 1960. Pierre Schapira remarked that "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 ...

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 ...

and was also able to build the algebraic and geometric tools adapted to his problems."

Awards and honors

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 Nevanlinna Prize (to be rename ...

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...

. He has been a member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, 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 Nati ...

since 1993. He received the

Schock Prize The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm Stockholm () is the capital and largest city of Sweden as well as the largest ...

in 1997 and the

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...

in 2003.

Notes

External links

*
Schock Prize citation1990 Interview
in the

AMS Notices ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...

Mikio Sato, a Visionary of Mathematics
by Pierre Schapira {{DEFAULTSORT:Sato, Mikio 1928 births Foreign associates of the National Academy of Sciences 20th-century Japanese mathematicians 21st-century Japanese mathematicians Living people Rolf Schock Prize laureates University of Tokyo alumni Wolf Prize in Mathematics laureates Osaka University faculty Kyoto University faculty Persons of Cultural Merit