12/03/31 22:21:50.05
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Mikio Sato, a Visionary of Mathematics Pierre Schapira NOTICES OF THE AMS FEBRUARY 2007
France was a strategic place to receive Sato’s ideas since they are based on those of both Jean Leray and Alexandre Grothendieck.
Like Leray, Sato understood that singularities have to be sought in the complex domain, even for the understanding of real phenomena.
Sato’s algebraic analysis is based on sheaf theory, a theory invented by Leray in 1944 when he was a prisoner of war, clarified by Cartan, and made extraordinarily efficient by Grothendieck and his formalism of derived categories and the six operations.
Sato, motivated by physics as usual, then tackled the analysis of the S-matrix in light of microlocal analysis.
With his two new students, M. Jimbo and T. Miwa, he explicitly constructed the solution of the n-points function of the Ising model in dimension 2 using Schlesinger’s classical theory of isomonodromic deformations of ordinary differential equations.
This naturally led him to the study of KdV-type nonlinear equations.
In 1981, with his wife Yasuko Sato, he interpreted the solutions of the KP-hierarchies as points of an infinite Grasmannian manifold and introduced his famous τ-function.
These results would be applied to other classes of equations and would have a great impact in mathematical physics in the study of integrable systems and field theory in dimension 2.
In parallel with his work in analysis and in mathematical physics, Sato obtained remarkable results in group theory and in number theory.
（つづく）