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]

Masaki Kashiwara
Born (1947-01-30) January 30, 1947
Yūki, Ibaraki, Japan
NationalityJapanese
Alma materUniversity of Tokyo (M.Sc., 1971)
Kyoto University (Ph.D., 1974)
Known foralgebraic analysis
microlocal analysis
D-modules
crystal bases
Riemann–Hilbert correspondence
Kazhdan–Lusztig conjecture
AwardsIyanaga Prize (1981)
Asahi Prize (1988)
Japan Academy Prize (1988)
Kyoto Prize in Mathematics (2018)
Chern Medal (2018) "For his outstanding and foundational contributions to algebraic analysis and representation theory sustained over a period of almost 50 years."
Scientific career
FieldsMathematics
InstitutionsKyoto University
Doctoral advisorMikio 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.[1]

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

Concepts and Theorems named after Kashiwara

List of books available in English
  • Seminar on micro-local analysis, by Victor Guillemin, Masaki Kashiwara, and Takahiro Kawai (1979), ISBN 978-0691082325
  • Systems of microdifferential equations, by Masaki Kashiwara; notes and translation by Teresa Monteiro Fernandes; introduction by Jean-Luc Brylinski (1983), ISBN 978-0817631383
  • 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 978-0691084138
  • 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, by Masaki Kashiwara, Pierre Schapira (1990), ISBN 978-3540518617
  • Topological field theory, primitive forms and related topics, by 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 and Pierre Schapira (2006), ISBN 978-3540279495

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 978-2856291269

Notes
  1. Pierre Schapira (2008). "Masaki Kashiwara and Algebraic Analysis". arXiv:0810.4875 [math.HO].
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