Masaki Kashiwara Edit Profile
His PhD thesis proves the rationality of the roots of b-functions (Bernstein-Sato polynomials), using D-module theory and resolution of singularities.
He was a student of Mikio Sato at the University of Tokyo. Kashiwara made leading contributions towards algebraic analysis, microlocal analysis, D-module theory, Hodge theory, sheaf theory and representation theory. Kashiwara and Sato established the foundations of the theory of systems of linear partial differential equations with analytic coefficients, introducing a cohomological approach that follows the spirit of Grothendieck theory of schemes.
Bernstein introduced a similar approach in the polynomial coefficients case. Kashiwara's master thesis states the foundations of D-modules theory. Kashiwara constructibility theorem Kashiwara index theorem Kashiwara–Malgrange filtration (after Kashiwara and Bernard Malgrange) Cauchy-Kowalevsky-Kashiwara theorem (after Kashiwara, Cauchy and Kovalevskaya ) Kashiwara operators Kashiwara crystal basis.
[Japan Academy; French Academy of Sciences]
He is a member of the French Academy of Sciences and of the Japan Academy.
1971 - 1973
1973 - 1977
1978 - 1984