Masaki Kashiwara

Masaki Kashiwara (柏原 正樹, Kashiwara Masaki, born January 30, 1947 in Yūki, Ibaraki) 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.

Masaki Kashiwara
Kashiwara at ICM Madrid in 2006
Born	(1947-01-30) January 30, 1947 Yūki, Ibaraki, Japan
Nationality	Japanese
Alma mater	University of Tokyo (MSc, 1971) Kyoto University (PhD, 1974)
Known for	algebraic analysis microlocal analysis D-modules crystal bases Riemann–Hilbert correspondence Kazhdan–Lusztig conjecture
Awards	Iyanaga Prize (1981) Asahi Prize (1988) Japan Academy Prize (1988) Kyoto Prize (2018) Chern Medal (2018)
Scientific career
Fields	Mathematics
Institutions	Kyoto University
Doctoral advisor	Mikio Sato

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 <Les débuts de la théorie des faisceaux> 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

External links

• Masaki Kashiwara at the Mathematics Genealogy Project
• Fifty years of Mathematics with Masaki Kashiwara, by Pierre Schapira
• List of Publications
• Photo
• Videos of Masaki Kashiwara in the AV-Portal of the German National Library of Science and Technology
• 2018 Kyoto Prize in Basic Sciences