Mikio Sato

Mikio Sato (佐藤 幹夫, Satō Mikio, born April 18, 1928) is a Japanese mathematician, who started the field of algebraic analysis, hyperfunctions, holonomic quantum fields and many more. He is known for a bunch of his extraditonally innovative works. Throughout his mathematical career, he was eager to revolutionise mathematics. He is recognised by many, including Pierre Schapira and Shigeru Iitaka, as the greatest mathematician of the 20th century alongside Grothendieck. He also independently discovered and created Grothendieck’s Cohomology theory in the process of developing his Hyperfunction theory. He was a plenary speaker at International Congress of Mathematicians, 1983, Warszawa.

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. Pierre Schapira remarks 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."[1]

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 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 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, Tetsuji Miwa, and Michio Jimbo, who have been called the "Sato School".[2]