Mikio Sato
 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (February 2013) |
Mikio Sato | |
|---|---|
| Born | April 18, 1928 Tokyo, Japan |
| Nationality | Japanese |
| Alma mater | University of Tokyo (BSc, 1952) (PhD, 1963) |
| Known for | Bernstein–Sato polynomials Sato–Tate conjecture Algebraic analysis holonomic quantum field |
| Awards | Rolf Schock Prize in Mathematics (1997) Wolf Prize (2003) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Kyoto University |
| Doctoral advisor | Shokichi Iyanaga |
| Doctoral students | Masaki Kashiwara Takahiro Kawai |
Mikio Sato (佐藤 幹夫, Satō Mikio, born April 18, 1928) is a Japanese mathematician known for founding the fields of algebraic analysis, hyperfunctions, and holonomic quantum fields. He is a professor at the Research Institute for Mathematical Sciences in Kyoto.
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.
His disciples include Masaki Kashiwara, Takahiro Kawai, Tetsuji Miwa, and Michio Jimbo, who have been called the "Sato School".[1]
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. 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).
He also contributed basic work to non-linear soliton theory, with the use of Grassmannians of infinite dimension.
In number theory, he and John Tate independently posed the Sato–Tate conjecture on L-functions around 1960.[2]
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."[3]
Awards and honors
Sato was a plenary speaker at the 1983 International Congress of Mathematicians in Warsaw.
He has been a member of the National Academy of Sciences since 1993. He received the Schock Prize in 1997 and the Wolf Prize in 2003.
Notes
- ^ 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
- ^ 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).
- ^ "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)
External links
- Mikio Sato at the Mathematics Genealogy Project
- Schock Prize citation
- 1990 Interview in the AMS Notices
- Mikio Sato, a Visionary of Mathematics by Pierre Schapira
- 1928 births
- Foreign associates of the National Academy of Sciences
- 20th-century Japanese mathematicians
- 21st-century Japanese mathematicians
- Living people
- Rolf Schock Prize laureates
- University of Tokyo alumni
- Wolf Prize in Mathematics laureates
- Osaka University faculty
- Kyoto University faculty
- Persons of Cultural Merit