Mikio Sato

Mikio Satō (Japanese佐藤 干 夫, Mikio Satō, born April 18, 1928 in Tokyo) is a Japanese mathematician who is mainly concerned with analysis, mathematical physics and is also known for a number theoretic conjecture.

Life

Satō was the son of a lawyer. During the Second World War, the family was bombed in Tokyo. Satō himself dragged during this time in a factory coals. 1945 to 1948 he attended the first high school, which was considered the elite school.

He then worked as a high school teacher to support his family, and remained a teacher until 1958. He studied from 1949 next to the University of Tokyo. Although his written work received high marks, but since he had failed exams, he could not be an assistant and studied further, this time theoretical physics studies at Shin'ichiro Tomonaga. Summer of 1957 he wrote a paper on the theory of hyperfunction to be accepted as a graduate student in the mathematics department. Shokichi Iyanaga made ​​sure that he was hired as an assistant (actually, he was assistant Kosaku Yoshida ) and 1963 he received his doctorate in Tokyo with him. In 1960 he was a lecturer at Tokyo University of Education, and from 1960 to 1962 he was at the Institute for Advanced Study ( Iyanaga had his work sent to André Weil). After that, he was a professor at the University of Osaka and Tokyo University. In 1970 he became a professor at the Research Institute for Mathematical Sciences ( RIMS) at the University of Kyoto. 1987 to 1991 he was director of RIMS. He is currently Professor Emeritus at the University of Kyoto.

In 1969 he was awarded the Asahi Prize in 1976 and the price of the Japanese Academy of Sciences. In 1984 he was awarded the Japanese Order of Culture and 1987 the Fujiwara Prize. Satō is a member of the U.S. National Academy of Sciences since 1993. In 1997 he was awarded the Rolf Schock Prize in 2003 and the Wolf Prize. In 1983 he gave a plenary lecture at the ICM in Warsaw ( monodromy theory and holonomic quantum fields -a new link in between mathematics and theoretical physics ) and in 1970 he was invited speaker at the ICM in Nice ( Regularity of hyperfunction solutions of partial differential equations ).

His doctoral counts Masaki Kashiwara.

Work

Satō is known primarily for the development of his theory of hyperfunctions, generalizations of distributions that are defined with the help of sheaf theory. If we define holomorphic functions in the upper and in the lower complex half-plane, then a hyperfunction defined as the difference on the real axis. It is invariant under addition of a holomorphic function and. He thus formulated a cohomological access (without any limit processes) to analysis parallel to Alexander Grothendieck about the same time. From his work on hyperfunctions to Sato's access to micro- local analysis of partial differential equations (via the " analytic wave front " of hypertext functions) and the algebraic theory of moduli ( expanded by his pupil Kashiwara 1969 in his dissertation ) developed. The idea of ​​the analogy of modules over commutative rings to vector bundles over manifolds, he formulated in 1960 in a colloquium lecture in Tokyo. Satō was ahead of his time with his ideas: They seemed analysts strange and were taken up relatively late and only in alternative formulations such as those of Hörmander. One exception was the French mathematician, where Sato's algebraic sheaf theoretical and access through the work of Leray, Cartan and Grothendieck came upon prepared ground.

Satō also worked on number theory. The up to now unproven Satō -Tate conjecture concerning the fine distribution of the solution of elliptic curves modulo numbers and say a statistical distribution function for the phases of the coefficients of the Hasse -Weil zeta functions of the advance curve, determine the fine distribution. In addition, he showed in 1962, as follow the Ramanujan -Peterson conjecture about coefficients of modular forms of the Weil conjectures, later proved by exactly Pierre Deligne.

Many of his motivations refers Satō from physics. In mathematical physics, he worked on Soliton Equations (partly with his wife Yasuko Satō ), which he regarded as Grassmann manifolds of infinite dimension. With Tetsuji Miwa and Michio Jimbo, he constructed explicitly - point correlation functions in the two-dimensional Ising model with the help of the deformation theory ( isomonodrom, ie with preserved monodromy ) of ordinary differential equations of Schlesinger from the 19th century.

Writings

• Theory of hyper functions. Volumes of 1.2, Journal of the Faculty of Sciences, University of Tokyo, Bd.8, 1959/60, p 139, 387
• T. Kawai, M. Kashiwara: Micro Functions and pseudo- differential equations. In: Komatsu (ed.): Hyper Functions and pseudo- differential equations. Proceedings Katata 1971, Springer- Verlag, Lecture Notes in Mathematics Vol 287, 1973, pp. 265-529.
• The Hierarchy and infinite dimensional Grassmannian manifolds. In: Theta Functions. Bowdoin 1985 Conference, Proceedings Symposia Pure Mathematics, Bd.49, Part 1, AMS 1989, p.51
• With Yasuko Sato: Soliton equations as dynamical systems on infinite dimensional Grassmannian manifolds. In: Nonlinear partial differential equations in applied sciences, Tokyo 1982, North Holland 1983, p.259.
• With T. Miwa, M. Jimbo: holonomic quantum fields. Part 1-5, Publications RIMS, Bd.14, 1978, p.223, Bd.15, 1979, pp. 201, 577, 871, Bd.16, 1980, S.531