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Mikio Sato is a Japanese mathematician, who started the field of algebraic analysis. 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.
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 origin and to expression in terms of sheaf theory. Further, it led to the theory of microfunctions, interest in microlocal aspects of linear partial differential equations and Fourier theory such as wave fronts, and ultimately to the current developments in D-module theory. Part of Mikio Sato's hyperfunction theory is the modern theory of holonomic systems: Partial Differential Equations over-determined to the point of having finite-dimensional spaces of solutions.
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.
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