Mikio Sato | |
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| Born | (1928-04-18)18 April 1928 Tokyo, Empire of Japan |
| Died | 9 January 2023(2023-01-09) (aged 94) |
| Alma mater | University of Tokyo (BSc, 1952; PhD, 1963) |
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| Fields | Mathematics |
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| Thesis | Theory of hyperfunctions (1963) |
| Doctoral advisor | Shokichi Iyanaga |
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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 ofalgebraic analysis,hyperfunctions, and holonomic quantum fields. He was a professor at theResearch Institute for Mathematical Sciences in Kyoto.
Born in Tokyo on 18 April 1928,[2] Sato studied at theUniversity of Tokyo, receiving his BSc in 1952 and PhD underShokichi Iyanaga in 1963.[3][4] He was a professor atOsaka University and theUniversity of Tokyo before moving to theResearch Institute for Mathematical Sciences (RIMS) attached toKyoto University in 1970.[3] He was director of RIMS from 1987 to 1991.[3]
His disciples includeMasaki Kashiwara,Takahiro Kawai,Tetsuji Miwa, as well asMichio Jimbo, who have been called the "Sato School".[5]
Sato died at home inKyoto on 9 January 2023, aged 94.[6][1]
Sato was known for his innovative work in a number of fields, such asprehomogeneous vector spaces andBernstein–Sato polynomials; and particularly for his hyperfunction theory.[3] This theory initially appeared as an extension of the ideas ofdistribution theory; it was soon connected to thelocal cohomology theory ofGrothendieck, for which it was an independent realisation in terms ofsheaf theory. Further, it led to the theory ofmicrofunctions andmicrolocal analysis in linearpartial differential equations andFourier theory, such as for wave fronts, and ultimately to the current developments inD-module theory.[2][7] Part of Sato's hyperfunction theory is the modern theory ofholonomic 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 withMichio Jimbo andTetsuji Miwa that developed the theory of holonomic quantum fields.[2] When Sato was awarded the 2002–2003Wolf 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-linearsoliton theory, with the use ofGrassmannians of infinite dimension.[3]
Innumber theory, he andJohn Tate independently posed theSato–Tate conjecture onL-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 treatanalysis asalgebraic geometry and was also able to build the algebraic and geometric tools adapted to his problems."[9]
Sato received the 1969Asahi Prize of Science, the 1976Japan Academy Prize, the 1984Person of Cultural Merits award of theJapanese Education Ministry, the 1997Schock Prize, and the 2002–2003Wolf Prize in Mathematics.[3]
Sato was a plenary speaker at the 1983International Congress of Mathematicians inWarsaw.[3] He was elected a foreign member of theNational Academy of Sciences in 1993.[3]
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