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{{short description|Japanese mathematician}}
{{short description|Japanese mathematician}}
{{Use mdy dates|date=August 2021}}
{{Use mdy dates|date=August 2021}}
{{more footnotes|date=February 2013}}
{{ Infobox scientist
{{ Infobox scientist
| name = Mikio Sato
| name = Mikio Sato
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==Education==
==Education==
Sato 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]] attached to [[Kyoto University]].
Sato studied at the [[University of Tokyo]], receiving his B.Sc. in 1952 and Ph.D. in [[physics]] as a student of [[Shin'ichiro Tomonaga]] in 1963.<ref name="notices"/> 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]], and [[Michio Jimbo]], who have been called the "Sato School".<ref>''Mikio Sato and Mathematical Physics'', Barry M. McCoy PRIMS Volume 47, Issue 1, 2011 http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=47&iss=1&rank=3&srch=searchterm%7CMikio+Sato</ref>
His disciples include [[Masaki Kashiwara]], [[Takahiro Kawai]], [[Tetsuji Miwa]], and [[Michio Jimbo]], who have been called the "Sato School".<ref>''Mikio Sato and Mathematical Physics'', Barry M. McCoy PRIMS Volume 47, Issue 1, 2011 http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=47&iss=1&rank=3&srch=searchterm%7CMikio+Sato</ref>


==Research==
==Research==
Sato 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 realization 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. 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]]).
Sato 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.<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 realization 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. 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 |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}}</ref>


He also contributed basic work to non-linear [[soliton]] theory, with the use of [[Grassmannian]]s of infinite dimension.
He 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>
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>
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==Awards and honors==
==Awards and honors==
Sato received the [[Asahi Prize of Science]] in 1969, the [[Japan Academy Prize (academics)|Japan Academy Prize]] in 1976, the [[Person of Cultural Merits]] award of the [[Japanese Education Ministry]] in 1984, the [[Schock Prize]] in 1997, and the [[Wolf Prize in Mathematics]] in 2002-2003.<ref name="notices"/>
Sato was a plenary speaker at the 1983 [[International Congress of Mathematicians]] in [[Warsaw]].

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"/>


He was 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.


== Notes ==
== Notes ==

Revision as of 06:27, 13 January 2023

Mikio Sato
Born(1928-04-18)April 18, 1928
Tokyo, Japan
DiedJanuary 9, 2023(2023-01-09) (aged 94)
NationalityJapanese
Alma materUniversity of Tokyo (BSc, 1952) (PhD, 1963)
Known forBernstein–Sato polynomials
Sato–Tate conjecture
Algebraic analysis
Holonomic quantum field
Hyperfunction
Prehomogeneous vector space
AwardsRolf Schock Prize in Mathematics (1997)
Wolf Prize (2003)
Scientific career
FieldsMathematics
InstitutionsKyoto University
Doctoral advisorShokichi Iyanaga
Doctoral studentsMasaki Kashiwara
Takahiro Kawai

Mikio Sato (佐藤 幹夫, Satō Mikio, April 18, 1928 - January 9, 2023[1]) 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.

Education

Sato studied at the University of Tokyo, receiving his B.Sc. in 1952 and Ph.D. in physics as a student of Shin'ichiro Tomonaga in 1963.[2] 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.[2] He was director of RIMS from 1987 to 1991.[2]

His disciples include Masaki Kashiwara, Takahiro Kawai, Tetsuji Miwa, and Michio Jimbo, who have been called the "Sato School".[3]

Research

Sato 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.[2] 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 realization 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. 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).[2]

He also contributed basic work to non-linear soliton theory, with the use of Grassmannians of infinite dimension.[2]

In number theory, he and John Tate independently posed the Sato–Tate conjecture on L-functions around 1960.[4]

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 as algebraic geometry and was also able to build the algebraic and geometric tools adapted to his problems."[5]

Awards and honors

Sato received the Asahi Prize of Science in 1969, the Japan Academy Prize in 1976, the Person of Cultural Merits award of the Japanese Education Ministry in 1984, the Schock Prize in 1997, and the Wolf Prize in Mathematics in 2002-2003.[2]

Sato was a plenary speaker at the 1983 International Congress of Mathematicians in Warsaw.[2] He was elected a foreign member of the National Academy of Sciences in 1993.[2]


Notes

  1. ^ @SpringerMath (January 11, 2023). "Very sad news: Prof Mikio Sato died in Kyoto on 9 Jan 2023, aged 94. May he rest in peace" (Tweet) – via Twitter.
  2. ^ a b c d e f g h i "Sato and Tate Receive 2002-2003 Wolf Prize". Notices of the American Mathematical Society. 50 (5): 569–570. 2003.
  3. ^ Mikio Sato and Mathematical Physics, Barry M. McCoy PRIMS Volume 47, Issue 1, 2011 http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=47&iss=1&rank=3&srch=searchterm%7CMikio+Sato
  4. ^ 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).
  5. ^ "Archived copy" (PDF). Archived from the original (PDF) on September 28, 2020. Retrieved September 20, 2020.{{cite web}}: CS1 maint: archived copy as title (link)
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