Masaki Kashiwara

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.^[1]

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. His PhD thesis proves the rationality of the roots of b-functions (Bernstein-Sato polynomials), using D-module theory and resolution of singularities.^[1]

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, Cauchy and Kovalevskaya )
• Kashiwara operators
• Kashiwara crystal basis

List of books available in English

• Seminar on micro-local analysis / by Victor W. Guillemin, Masaki Kashiwara, and Takahiro Kawai (1979), ISBN 978-0691082325
• Systems of microdifferential equations / Masaki Kashiwara ; notes and translation by Teresa Monteiro Fernandes ; introduction by Jean-Luc Brylinski (1983), ISBN 978-0817631383
• Introduction to microlocal analysis / M. Kashiwara (1986)
• Foundations of algebraic analysis / by Masaki Kashiwara, Takahiro Kawai, and Tatsuo Kimura ; translated by Goro Kato (1986), ISBN 978-0691084138
• Algebraic analysis : papers dedicated to Professor Mikio Sato on the occasion of his sixtieth birthday / edited by Masaki Kashiwara, Takahiro Kawai (1988), ISBN 978-0124004665
• Sheaves on manifolds : with a short history <Les débuts de la théorie des faisceaux> by Christian Houzel / Masaki Kashiwara, Pierre Schapira (1990), ISBN 978-3540518617
• Topological field theory, primitive forms and related topics / Masaki Kashiwara et al.(1998), ISBN 978-0817639754
• Physical combinatorics / Masaki Kashiwara, Tetsuji Miwa, editors (2000), ISBN 978-1461271215
• MathPhys Odyssey 2001 : integrable models and beyond : in honor of Barry M. McCoy / Masaki Kashiwara, Tetsuji Miwa, editors (2002), ISBN 978-0817642600
• D-modules and microlocal calculus / Masaki Kashiwara ; translated by Mutsumi Saito (2003), ISBN 978-0821827666
• Categories and sheaves / Masaki Kashiwara, Pierre Schapira (2006), ISBN 978-3540279495

List of books available in French

• Bases cristallines des groupes quantiques / Masaki Kashiwara (rédigé par Charles Cochet) ; Cours Spécialisés 9 (2002), viii+115 pages, ISBN 978-2856291269

Notes

1. Pierre Schapira. "Masaki Kashiwara and Algebraic Analysis" (PDF).

External links

• Masaki Kashiwara at the Mathematics Genealogy Project
• Masaki Kashiwara and Algebraic Analysis, by Pierre Schapira
• List of Publications
• Photo