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{{nihongo|'''Mikio Sato'''|佐藤 幹夫|Satō Mikio|extra=born April 18, 1928}} is a [[Japan]]ese [[mathematician]], who started the field of [[algebraic analysis]]. He studied at the [[University of Tokyo]] and then did graduate study in [[physics]] as a student of [[Shin'ichiro Tomonaga]]. Since 1970, Sato has been professor at the [[Research Institute for Mathematical Sciences]], of [[Kyoto University]].
{{nihongo|'''Mikio Sato'''|佐藤 幹夫|Satō Mikio|extra=born April 18, 1928}} is a [[Japan]]ese [[mathematician]], who started the field of [[algebraic analysis]]. He studied at the [[University of Tokyo]] and then did graduate study in [[physics]] as a student of [[Shin'ichiro Tomonaga]]. Since 1970, Sato has been professor at the [[Research Institute for Mathematical Sciences]], of [[Kyoto University]].


He is known for his innovative work in a number of fields, such as [[prehomogeneous vector space]]s and [[Bernstein–Sato polynomial]]s; and particularly for his [[hyperfunction]] [[theory]]. This theory initially appeared as an extension of the ideas of [[distribution (mathematics)|distribution]] theory; it was soon connected to the [[local cohomology]] theory of [[Grothendieck]], for which it was an independent origin and to expression in terms of [[sheaf (mathematics)|sheaf]] theory. Further, it led to the theory of [[microfunction]]s, interest in ''microlocal'' aspects of linear [[partial differential equation]]s and [[Harmonic analysis|Fourier theory]] such as ''wave fronts'', and ultimately to the current developments in [[D-module]] theory. Part of Mikio Sato's hyperfunction theory is the modern theory of [[holonomic system]]s: [[Partial Differential Equations]] (PDEs) over-determined to the point of having [[Finite-dimensional_vector_space|finite-dimensional spaces]] of solutions.
He is known for his innovative work in a number of fields, such as [[prehomogeneous vector space]]s and [[Bernstein–Sato polynomial]]s; and particularly for his [[hyperfunction]] [[theory]]. This theory initially appeared as an extension of the ideas of [[distribution (mathematics)|distribution]] theory; it was soon connected to the [[local cohomology]] theory of [[Grothendieck]], for which it was an independent origin and to expression in terms of [[sheaf (mathematics)|sheaf]] theory. Further, it led to the theory of [[microfunction]]s, interest in ''microlocal'' aspects([[Microlocal analysis]]) of linear [[partial differential equation]]s and [[Harmonic analysis|Fourier theory]] such as ''wave fronts'', and ultimately to the current developments in [[D-module]] theory. Part of Mikio Sato's hyperfunction theory is the modern theory of [[holonomic system]]s: [[Partial Differential Equations]] (PDEs) over-determined to the point of having [[Finite-dimensional_vector_space|finite-dimensional spaces]] of solutions([[Algebraic analysis]]).


He also contributed basic work to non-linear [[soliton]] theory, with the use of [[Grassmannian]]s of infinite dimension. In [[number theory]], he is known for the [[Sato–Tate conjecture]] on [[L-function]]s.
He also contributed basic work to non-linear [[soliton]] theory, with the use of [[Grassmannian]]s of infinite dimension. In [[number theory]], he is known for the [[Sato–Tate conjecture]] on [[L-function]]s.


He has been a member of the [[United States National Academy of Sciences|National Academy of Sciences]] since 1993. He also received the [[Schock Prize]] in 1997 and the [[Wolf Prize]] in 2003.
He has been a member of the [[United States National Academy of Sciences|National Academy of Sciences]] since 1993. He also received the [[Schock Prize]] in 1997 and the [[Wolf Prize]] in 2003.

His disciples include [[Masaki Kashiwara]], Takahiro Kawai<ref>Takahiro Kawai https://de.wikipedia.org/wiki/Takahiro_Kawai</ref>, Tetsuji Miwa<ref>Tetsuji Miwa https://de.wikipedia.org/wiki/Tetsuji_Miwa</ref>, [[Michio Jimbo]], etc. There were things sometimes called "Sato School".

== Notes ==
{{Reflist}}


==External links==
==External links==

Revision as of 01:07, 21 June 2017

Mikio Sato
Born (1928-04-18) April 18, 1928 (age 96)
Tokyo, Japan
NationalityJapan
Alma materUniversity of Tokyo (B.Sc., 1952) (Ph.D., 1963)
Known forBernstein–Sato polynomials
Sato-Tate conjecture
AwardsRolf Schock Prize in Mathematics (1997)
Wolf Prize in Mathematics (2003)
Scientific career
FieldsMathematics
InstitutionsKyoto University
Doctoral advisorShokichi Iyanaga
Doctoral studentsMasaki Kashiwara
Motohico Mulase

Mikio Sato (佐藤 幹夫, Satō Mikio, born April 18, 1928) is a Japanese mathematician, who started the field of algebraic analysis. He studied at the University of Tokyo and then did graduate study in physics as a student of Shin'ichiro Tomonaga. Since 1970, Sato has been professor at the Research Institute for Mathematical Sciences, of Kyoto University.

He is 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 origin and to expression in terms of sheaf theory. Further, it led to the theory of microfunctions, interest in microlocal aspects(Microlocal analysis) of linear partial differential equations and Fourier theory such as wave fronts, and ultimately to the current developments in D-module theory. Part of Mikio Sato's hyperfunction theory is the modern theory of holonomic systems: Partial Differential Equations (PDEs) over-determined to the point of having finite-dimensional spaces of solutions(Algebraic analysis).

He also contributed basic work to non-linear soliton theory, with the use of Grassmannians of infinite dimension. In number theory, he is known for the Sato–Tate conjecture on L-functions.

He has been a member of the National Academy of Sciences since 1993. He also received the Schock Prize in 1997 and the Wolf Prize in 2003.

His disciples include Masaki Kashiwara, Takahiro Kawai[1], Tetsuji Miwa[2], Michio Jimbo, etc. There were things sometimes called "Sato School".

Notes

  1. ^ Takahiro Kawai https://de.wikipedia.org/wiki/Takahiro_Kawai
  2. ^ Tetsuji Miwa https://de.wikipedia.org/wiki/Tetsuji_Miwa
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