Masaki Kashiwara

Masaki Kashiwara (柏原 正樹) is a Japanese mathematician. 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's theory of schemes. Bernstein introduced a similar approach in the polynomial coefficients case. Kashiwara's master thesis states the foundations of D-module theory. 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 plenary speaker at International Congress of Mathematicians, 1978, Helsinki and an invited speaker, 1990, Kyoto.

He is a member of the French Academy of Sciences and of the Japan Academy.

Concepts and Theorems named after Kashiwara

 * Kashiwara constructibility theorem
 * Kashiwara index theorem
 * Kashiwara–Malgrange filtration (after Kashiwara and Bernard Malgrange)
 * Cauchy-Kowalevsky-Kashiwara theorem (after Kashiwara, Augustin-Louis Cauchy and Sofya Kovalevskaya )
 * Kashiwara operators
 * Kashiwara crystal basis

List of books available in English

 * Seminar on micro-local analysis, by Victor Guillemin, Masaki Kashiwara, and Takahiro Kawai (1979), ISBN 978-0-691-08232-5
 * Systems of microdifferential equations, by Masaki Kashiwara; notes and translation by Teresa Monteiro Fernandes; introduction by Jean-Luc Brylinski (1983), ISBN 978-0-8176-3138-3
 * Introduction to microlocal analysis, by Masaki Kashiwara (1986)
 * Foundations of algebraic analysis, by Masaki Kashiwara, Takahiro Kawai, and Tatsuo Kimura; translated by Goro Kato (1986), ISBN 978-0-691-08413-8
 * Algebraic analysis : papers dedicated to Professor Mikio Sato on the occasion of his sixtieth birthday, edited by Masaki Kashiwara, Takahiro Kawai (1988), ISBN 978-0-12-400466-5
 * Sheaves on manifolds : with a short history  by Christian Houzel, by Masaki Kashiwara, Pierre Schapira (1990), ISBN 978-3-540-51861-7
 * Topological field theory, primitive forms and related topics, by Masaki Kashiwara et al.(1998), ISBN 978-0-8176-3975-4
 * Physical combinatorics, Masaki Kashiwara, Tetsuji Miwa, editors (2000), ISBN 978-1-4612-7121-5
 * MathPhys Odyssey 2001: integrable models and beyond: in honor of Barry M. McCoy, Masaki Kashiwara, Tetsuji Miwa, editors (2002), ISBN 978-0-8176-4260-0
 * D-modules and microlocal calculus, Masaki Kashiwara; translated by Mutsumi Saito (2003), ISBN 978-0-8218-2766-6
 * Categories and sheaves, Masaki Kashiwara and Pierre Schapira (2006), ISBN 978-3-540-27949-5

List of books available in French

 * Bases cristallines des groupes quantiques, by Masaki Kashiwara (rédigé par Charles Cochet); Cours Spécialisés 9 (2002), viii+115 pages, ISBN 978-2-85629-126-9