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{{Short description|Japanese mathematician (1928–2023)}}
'''Mikio Sato''' ([[Japanese language|Japanese]]: 佐藤 幹夫 ''Sato Mikio''; 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]]. From 1970 Sato has been professor at the [[Research Institute for Mathematical Sciences]], of [[Kyoto University]].
{{Use British English|date=January 2023}}
{{Use dmy dates|date=January 2023}}
{{Infobox scientist
| name = Mikio Sato
| image = File:Mikio Sato.jpg
| image_size =
| caption =
| birth_date = {{birth date|1928|04|18|df=yes}}
| birth_place = Tokyo, Empire of Japan<!-- DO NOT LINK, see [[MOS:GEOLINK]] for further guidance -->
| death_date = {{death date and age|2023|01|09|1928|04|1|8|df=yes}}
| death_place = [[Kyoto]], Japan<ref name=jiji>{{citation |title=佐藤幹夫氏死去（京都大名誉教授） | newspaper=時事通信社 |date=January 18, 2023 |url=https://www.jiji.com/jc/article?k=2023011600560}}</ref>
| fields = Mathematics
| workplaces = {{Plainlist|
* [[Kyoto University]]
* [[University of Tokyo]]
* [[Osaka University]]
}}
| alma_mater = [[University of Tokyo]] (BSc, 1952; PhD, 1963)
| thesis_title = Theory of hyperfunctions
| thesis_year = 1963
| doctoral_advisor = [[Shokichi Iyanaga]]
| doctoral_students = {{Flatlist|
* [[Masaki Kashiwara]]
* [[Takahiro Kawai]]
}}
| known_for = {{Plainlist|
* [[Bernstein–Sato polynomial]]s
* [[Sato–Tate conjecture]]
* [[Algebraic analysis]]
* Holonomic quantum field
* [[Hyperfunction]]
* [[Prehomogeneous vector space]]
}}
| awards = {{Plainlist|
* [[Asahi Prize of Science]] (1969)
* [[Japan Academy Prize (academics)|Japan Academy Prize]] (1976)
* [[Person of Cultural Merits]] (1984)
* [[Rolf Schock Prize]] in Mathematics (1997)
* [[Wolf Prize in Mathematics|Wolf Prize]] (2003)
}}
}}


{{nihongo|'''Mikio Sato'''|佐藤 幹夫|Satō Mikio|extra=18 April 1928 – 9 January 2023|lead=yes}} was a Japanese mathematician known for founding the fields of [[algebraic analysis]], [[hyperfunction]]s, and holonomic quantum fields. He was a professor at the [[Research Institute for Mathematical Sciences]] in Kyoto.
⚫
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 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. It led further 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 that is the modern theory of [[holonomic]] systems: PDEs over-determined to the point of having finite-dimensional spaces of solutions.


==Biography==
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.
Born in Tokyo on 18 April 1928,<ref name="mactutor">{{cite web |title=Mikio Sato – Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Sato/ |website=[[MacTutor History of Mathematics archive]] |publisher=[[University of St Andrews]] |access-date=15 January 2023 |language=en}}</ref> Sato studied at the [[University of Tokyo]], receiving his BSc in 1952 and PhD under [[Shokichi Iyanaga]] in 1963.<ref name="notices"/><ref>{{MathGenealogy |id=19282}}</ref> He was a professor at [[Osaka University]] and the [[University of Tokyo]] before moving to the [[Research Institute for Mathematical Sciences]] (RIMS) attached to [[Kyoto University]] in 1970.<ref name="notices"/> He was director of RIMS from 1987 to 1991.<ref name="notices"/>


His disciples include [[Masaki Kashiwara]], [[Takahiro Kawai]], [[Tetsuji Miwa]], as well as [[Michio Jimbo]], who have been called the "Sato School".<ref>{{cite journal |title=Mikio Sato and Mathematical Physics |first1=Barry M. |last1=McCoy |journal=Publications of the Research Institute for Mathematical Sciences |date=24 March 2011 |volume=47 |issue=1 |pages=19–28 |doi=10.2977/prims/30 |url=https://ems.press/journals/prims/articles/4467 |access-date=16 January 2023 |language=en |issn=0034-5318|doi-access=free }}</ref>
He is a member of the [[United States National Academy of Sciences|National Academy of Sciences]] since 1993. He received the [[Schock Prize]] in 1997, and the [[Wolf Prize]] in 2003.

Sato died at home in [[Kyoto]] on 9 January 2023, aged 94.<ref>{{Cite web |title=The untimely passing of Professor Emeritus Sato Mikio |url=https://www.kurims.kyoto-u.ac.jp/en/notice3.html |accessdate=13 January 2023}}, Notice: Research Institute for Mathematical Sciences, Kyoto University (2023/01/13)</ref><ref name=jiji/>

==Research==
⚫
Sato was 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.<ref name="notices"/> 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 realisation in terms of [[sheaf (mathematics)|sheaf]] theory. Further, it led to the theory of [[microfunction]]s and [[microlocal analysis]] in linear [[partial differential equation]]s and [[Harmonic analysis|Fourier theory]], such as for wave fronts, and ultimately to the current developments in [[D-module|''D''-module]] theory.<ref name="mactutor"/><ref>{{cite journal | title = Professor Mikio Sato and Microlocal Analysis
| last1 = Kashiwara | first1 = Masaki
| last2 = Kawai | first2 = Takahiro
| author1-link = Masaki Kashiwara
| author2-link = Takahiro Kawai
| journal = Publications of the Research Institute for Mathematical Sciences | via = EMS-PH
| year = 2011 | volume = 47 | issue = 1 | pages = 11–17
| url = http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=47&iss=1&rank=2
| doi = 10.2977/PRIMS/29
| doi-access = free
}}</ref> Part of Sato's hyperfunction theory is the modern theory of [[holonomic system]]s: PDEs overdetermined to the point of having finite-dimensional spaces of solutions ([[algebraic analysis]]).<ref name="notices">{{cite journal |first1=Allyn |last1=Jackson |title=Sato and Tate Receive 2002–2003 Wolf Prize |journal=[[Notices of the American Mathematical Society]] |volume=50 |issue=5 |year=2003 |pages=569–570 |url=https://www.ams.org/notices/200305/comm-wolf.pdf }}</ref>

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.<ref name="mactutor"/> When Sato was awarded the 2002–2003 [[Wolf Prize in Mathematics]], 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."<ref name="mactutor"/><ref name="notices"/> Sato also contributed basic work to non-linear [[soliton]] theory, with the use of [[Grassmannian]]s of infinite dimension.<ref name="notices"/>

In [[number theory]], he and [[John Tate (mathematician)|John Tate]] independently posed the [[Sato–Tate conjecture]] on [[L-function|''L''-function]]s around 1960.<ref>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).</ref>

[[Pierre Schapira (mathematician)|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 [[mathematical analysis|analysis]] as [[algebraic geometry]] and was also able to build the algebraic and geometric tools adapted to his problems."<ref name="Schapira 2007">{{cite journal |last1=Schapira |first1=Pierre |title=Mikio Sato, a Visionary of Mathematics |journal=[[Notices of the American Mathematical Society]] |date=February 2007 |volume=54 |issue=2 |pages=243–245 |url=https://www.ams.org/notices/200702/comm-schapira.pdf |access-date=16 January 2023 |archive-date=28 September 2020 |archive-url=https://web.archive.org/web/20200928023318/https://webusers.imj-prg.fr/~pierre.schapira/mispapers/Sato.pdf }}</ref>

==Awards and honours==
Sato received the 1969 [[Asahi Prize of Science]], the 1976 [[Japan Academy Prize (academics)|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]].<ref name="notices"/>

Sato was a plenary speaker at the 1983 [[International Congress of Mathematicians]] in [[Warsaw]].<ref name="notices"/> He was elected a foreign member of the [[United States National Academy of Sciences|National Academy of Sciences]] in 1993.<ref name="notices"/>

== Notes ==
{{Reflist}}


==External links==
==External links==
⚫
* [https://web.archive.org/web/20061214094433/http://www.math.uu.se/~kiselman/sato1997.html Schock Prize citation]
*{{MathGenealogy |id=19282}}
* [https://www.ams.org/notices/200702/fea-sato-2.pdf 1990 Interview] in the ''[[AMS Notices]]''
⚫
*[http://www.math.uu.se/~Kiselman/sato1997.html Schock Prize citation]
*[http://www.ams.org/notices/200702/fea-sato-2.pdf 1990 Interview] in the [[AMS Notices]]
* [https://www.ams.org/notices/200702/comm-schapira.pdf Mikio Sato, a Visionary of Mathematics] by Pierre Schapira
*[http://www.ams.org/notices/200702/comm-schapira.pdf Mikio Sato, a Visionary of Mathematics] by Pierre Schapira
* [https://www.ams.org/journals/notices/202405/noti2931/noti2931.html ''Memories of Mikio Sato (1928–2023)''], [[AMS Notices]], (May 2024)


{{Schock Prize laureates}}
{{Schock Prize laureates}}
{{Wolf Prize in Mathematics}}
{{Wolf Prize in Mathematics}}


{{Authority control}}
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{{DEFAULTSORT:Sato, Mikio}}


⚫
{{DEFAULTSORT:Sato, Mikio}}
[[Category:1928 births]]
[[Category:1928 births]]
[[Category:Members of the National Academy of Sciences]]
[[Category:2023 deaths]]
[[Category:20th-century mathematicians]]
[[Category:20th-century Japanese mathematicians]]
[[Category:Japanese mathematicians]]
[[Category:21st-century Japanese mathematicians]]
[[Category:Living people]]
[[Category:Foreign associates of the National Academy of Sciences]]
[[Category:Academic staff of Kyoto University]]
[[Category:Academic staff of Osaka University]]
[[Category:Persons of Cultural Merit]]
[[Category:Rolf Schock Prize laureates]]
[[Category:Rolf Schock Prize laureates]]
[[Category:Scientists from Tokyo]]
[[Category:University of Tokyo alumni]]
[[Category:University of Tokyo alumni]]
[[Category:Academic staff of the University of Tokyo]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Wolf Prize in Mathematics laureates]]

[[de:Mikio Satō]]
[[es:Mikio Satō]]
[[fr:Mikio Satō]]
[[nl:Mikio Sato]]
[[ja:佐藤幹夫 (数学者)]]
[[sk:Mikio Satō]]
[[fi:Mikio Satō]]
[[zh:佐藤幹夫]]

Latest revision as of 21:49, 24 June 2024

Mikio Sato
Born(1928-04-18)18 April 1928
Tokyo, Empire of Japan
Died9 January 2023(2023-01-09) (aged 94)
Kyoto, Japan[1]
Alma materUniversity of Tokyo (BSc, 1952; PhD, 1963)
Known for
Awards
Scientific career
FieldsMathematics
Institutions
Thesis Theory of hyperfunctions  (1963)
Doctoral advisorShokichi Iyanaga
Doctoral students

Mikio Sato (Japanese: 佐藤 幹夫, Hepburn: Satō Mikio, 18 April 1928 – 9 January 2023) 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 in Kyoto.

Biography

[edit]

Born in Tokyo on 18 April 1928,[2] Sato studied at the University of Tokyo, receiving his BSc in 1952 and PhD under Shokichi Iyanaga in 1963.[3][4] He was a professor at Osaka University and the University of Tokyo before moving to the Research Institute for Mathematical Sciences (RIMS) attached to Kyoto University in 1970.[3] He was director of RIMS from 1987 to 1991.[3]

His disciples include Masaki Kashiwara, Takahiro Kawai, Tetsuji Miwa, as well as Michio Jimbo, who have been called the "Sato School".[5]

Sato died at home in Kyoto on 9 January 2023, aged 94.[6][1]

Research

[edit]

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.[3] 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 equations and Fourier theory, such as for wave fronts, and ultimately to the current developments in D-module theory.[2][7] 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).[3]

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.[2] When Sato was awarded the 2002–2003 Wolf Prize in Mathematics, 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."[2][3] Sato also contributed basic work to non-linear soliton theory, with the use of Grassmannians of infinite dimension.[3]

In number theory, he and John Tate independently posed the Sato–Tate conjecture on L-functions around 1960.[8]

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 as algebraic geometry and was also able to build the algebraic and geometric tools adapted to his problems."[9]

Awards and honours

[edit]

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.[3]

Sato was a plenary speaker at the 1983 International Congress of Mathematicians in Warsaw.[3] He was elected a foreign member of the National Academy of Sciences in 1993.[3]

Notes

[edit]
  1. ^ a b "佐藤幹夫氏死去（京都大名誉教授）", 時事通信社, 18 January 2023
  2. ^ a b c d "Mikio Sato – Biography". MacTutor History of Mathematics archive. University of St Andrews. Retrieved 15 January 2023.
  3. ^ a b c d e f g h i j Jackson, Allyn (2003). "Sato and Tate Receive 2002–2003 Wolf Prize" (PDF). Notices of the American Mathematical Society. 50 (5): 569–570.
  4. ^ Mikio Sato at the Mathematics Genealogy Project
  5. ^ McCoy, Barry M. (24 March 2011). "Mikio Sato and Mathematical Physics". Publications of the Research Institute for Mathematical Sciences. 47 (1): 19–28. doi:10.2977/prims/30. ISSN 0034-5318. Retrieved 16 January 2023.
  6. ^ "The untimely passing of Professor Emeritus Sato Mikio". Retrieved 13 January 2023., Notice: Research Institute for Mathematical Sciences, Kyoto University (2023/01/13)
  7. ^ Kashiwara, Masaki; Kawai, Takahiro (2011). "Professor Mikio Sato and Microlocal Analysis". Publications of the Research Institute for Mathematical Sciences. 47 (1): 11–17. doi:10.2977/PRIMS/29 – via EMS-PH.
  8. ^ 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).
  9. ^ Schapira, Pierre (February 2007). "Mikio Sato, a Visionary of Mathematics" (PDF). Notices of the American Mathematical Society. 54 (2): 243–245. Archived from the original (PDF) on 28 September 2020. Retrieved 16 January 2023.
[edit]
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