is a Japanese mathematician. He was a student of

Mikio Sato is a Japanese mathematician known for founding the fields of algebraic analysis, hyperfunctions, and holonomic quantum fields. He is a professor at the Research Institute for Mathematical Sciences in Kyoto. Education Sato studied at the Unive ...

at the

University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

. Kashiwara made leading contributions towards

algebraic analysis Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctio ...

microlocal analysis In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes genera ...

, ''D''-module theory,

Hodge theory In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every cohom ...

sheaf theory In mathematics, a sheaf is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could ...

and

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

. Kashiwara and Sato established the foundations of the theory of systems of linear partial differential equations with analytic coefficients, introducing a

cohomological In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...

approach that follows the spirit of Grothendieck's theory of schemes.

Bernstein Bernstein is a common surname in the German language, meaning "amber" (literally "burn stone"). The name is used by both Germans and Jews, although it is most common among people of Ashkenazi Jewish heritage. The German pronunciation is , but in E ...

introduced a similar approach in the

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

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 polynomial In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by and , . It is also known as the b-function, the b-polynomial, and the Bernstein polynomial, though it is not related ...

s), using ''D''-module theory and

resolution of singularities In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety ''V'' has a resolution, a non-singular variety ''W'' with a proper birational map ''W''→''V''. For varieties over fields of characterist ...

. He was a plenary speaker at International Congress of Mathematicians, 1978,

Helsinki Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of U ...

and an invited speaker, 1990,

Kyoto Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ci ...

. He is a member of the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

and of the

Japan Academy The Japan Academy (Japanese: 日本学士院, ''Nihon Gakushiin'') is an honorary organisation and science academy founded in 1879 to bring together leading Japanese scholars with distinguished records of scientific achievements. The Academy is c ...

Concepts and Theorems named after Kashiwara

Kashiwara constructibility theorem file:Kashiwara City Office, Osaka pref01.JPG, 270px, Kashiwara City Hall is a city located in Osaka Prefecture, Japan. , the city had an estimated population of 67,698 in 32007 households and a population density of . The total area of the city ...

Kashiwara index theorem 270px, Kashiwara City Hall is a city located in Osaka Prefecture, Japan. , the city had an estimated population of 67,698 in 32007 households and a population density of . The total area of the city is . Geography Kashiwara is located about ...

* Kashiwara–Malgrange filtration (after Kashiwara and Bernard Malgrange) * Cauchy-Kowalevsky-Kashiwara theorem (after Kashiwara,

Augustin-Louis Cauchy Baron Augustin-Louis Cauchy (, ; ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He ...

and

Sofya Kovalevskaya Sofya Vasilyevna Kovalevskaya (russian: link=no, Софья Васильевна Ковалевская), born Korvin-Krukovskaya ( – 10 February 1891), was a Russian mathematician who made noteworthy contributions to analysis, partial differe ...

) * Kashiwara operators * Kashiwara crystal basis

List of books available in English

*''Seminar on micro-local analysis'', by

Victor Guillemin Victor William Guillemin (born 1937 in Boston) is an American mathematician working in the field of symplectic geometry, who has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics. He is a ten ...

, Masaki Kashiwara, and Takahiro Kawai (1979), *''Systems of microdifferential equations'', by Masaki Kashiwara; notes and translation by Teresa Monteiro Fernandes; introduction by

Jean-Luc Brylinski Jean-Luc Brylinski (born in 1951) is a French- American mathematician. Educated at the Lycée Pasteur and the École Normale Supérieure in Paris, after an appointment as researcher with the C. N. R. S., he became a Professor of Mathematics at ...

(1983), *''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), *''Algebraic analysis : papers dedicated to Professor Mikio Sato on the occasion of his sixtieth birthday'', edited by Masaki Kashiwara, Takahiro Kawai (1988), *''Sheaves on manifolds'' : with a short history by Christian Houzel, by Masaki Kashiwara, Pierre Schapira (1990), *''Topological field theory, primitive forms and related topics'', by Masaki Kashiwara ''et al.''(1998), *''Physical combinatorics'', Masaki Kashiwara,

Tetsuji Miwa Tetsuji Miwa (三輪哲二, ''Miwa Tetsuji''; born 10 February 1949 in Tokyo) is a Japanese mathematician, specializing in mathematical physics. Miwa received his undergraduate degree in 1971 and his master's degree in 1973 from the University o ...

, editors (2000), *''MathPhys Odyssey 2001'': integrable models and beyond: in honor of Barry M. McCoy, Masaki Kashiwara,

, editors (2002), *''D-modules and microlocal calculus'', Masaki Kashiwara; translated by Mutsumi Saito (2003), *''Categories and sheaves'', Masaki Kashiwara and Pierre Schapira (2006),

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,

Notes

External links

*
Fifty years of Mathematics with Masaki Kashiwara
by Pierre Schapira
Videos of Masaki Kashiwara
in the AV-Portal of the

German National Library of Science and Technology The German National Library of Science and Technology (german: Technische Informationsbibliothek), abbreviated TIB, is the national library of the Federal Republic of Germany for all fields of engineering, technology, and the natural sciences. I ...

*201
Kyoto Prize in Basic Sciences
1947 births Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians University of Tokyo alumni Academic staff of Kyoto University Academic staff of Nagoya University Members of the Japan Academy Members of the French Academy of Sciences Kyoto laureates in Basic Sciences {{asia-mathematician-stub