is a Japan

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

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, who started the field of algebraic analysis

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 microfunctions.-See also:...

. He studied at the University of Tokyo

University of Tokyo

, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...

, and then did graduate study in physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 as a student of Shin'ichiro Tomonaga. From 1970 Sato has been professor at the Research Institute for Mathematical Sciences

Research Institute for Mathematical Sciences

The is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. The institute is often abbreviated as RIMS...

, of Kyoto University

Kyoto University

, or is a national university located in Kyoto, Japan. It is the second oldest Japanese university, and formerly one of Japan's Imperial Universities.- History :...

.

He is known for his innovative work in a number of fields, such as prehomogeneous vector space

Prehomogeneous vector space

In mathematics, a prehomogeneous vector space is a finite-dimensional vector space V together with a subgroup G of GL such that G has an open dense orbit in V. Prehomogeneous vector spaces were introduced by Mikio Sato in 1970 and have many applications in geometry, number theory and analysis, as...

s and Bernstein–Sato polynomial

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 to the Bernstein polynomials used in approximation...

s; and particularly for his hyperfunction

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...

 theory. This initially appeared as an extension of the ideas of distribution

Distribution (mathematics)

In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...

 theory; it was soon connected to the local cohomology

Local cohomology

In mathematics, local cohomology is a chapter of homological algebra and sheaf theory introduced into algebraic geometry by Alexander Grothendieck. He developed it in seminars in 1961 at Harvard University, and 1961-2 at IHES. It was later written up as SGA2...

 theory of Grothendieck, for which it was an independent origin, and to expression in terms of sheaf

Sheaf (mathematics)

In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of...

 theory. It led further to the theory of microfunctions, interest in microlocal aspects of linear partial differential equation

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s and Fourier theory

Harmonic analysis

Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...

 such as wave fronts, and ultimately to the current developments in D-module

D-module

In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations...

 theory. Part of that is the modern theory of holonomic

Holonomic

In mathematics and physics, the term holonomic may occur with several different meanings.-Holonomic basis:A holonomic basis for a manifold is a set of basis vectors ek for which all Lie derivatives vanish:[e_j,e_k]=0 \,...

 systems: PDEs over-determined to the point of having finite-dimensional spaces of solutions.

He also contributed basic work to non-linear soliton

Soliton

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

 theory, with the use of Grassmannian

Grassmannian

In mathematics, a Grassmannian is a space which parameterizes all linear subspaces of a vector space V of a given dimension. For example, the Grassmannian Gr is the space of lines through the origin in V, so it is the same as the projective space P. The Grassmanians are compact, topological...

s of infinite dimension. In number theory

Number theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

 he is known for the Sato–Tate conjecture on L-function

L-function

The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad generalisations of the Riemann zeta function and the L-series for a Dirichlet character are constructed, and their general properties, in most cases...

s.

He is a member of the National Academy of Sciences

United States National Academy of Sciences

The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...

 since 1993. He received the Schock Prize

Schock prize

The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock . The prizes were first awarded in Stockholm, Sweden, in 1993 and have been awarded every two years since...

 in 1997, and the Wolf Prize in 2003.

External links

• Schock Prize citation
• 1990 Interview in the AMS Notices
• Mikio Sato, a Visionary of Mathematics by Pierre Schapira