Morihiko Saitō (, ''Saitō Morihiko'', born 1961) is a Japanese mathematician, specializing in

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 microfuncti ...

and algebraic geometry.

Education and career

After graduating from Aiko High School in

Matsuyama 270px, Matsuyama City Hall 270px, Ehime Prefectural Capital Building is the capital city of Ehime Prefecture on the island of Shikoku in Japan and also Shikoku's largest city. , the city had an estimated population of 505,948 in 243541 househ ...

, Saito completed undergraduate study in mathematics 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 ...

and in 1979 completed the master's program there. In 1986 he received his D.Sc. from

Kyoto University , mottoeng = Freedom of academic culture , established = , type = Public (National) , endowment = ¥ 316 billion (2.4 billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff = 3,978 (Total Staff) , students = 22 ...

. After working as a research assistant at Kyoto University's

Research Institute for Mathematical Sciences The is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. RIMS was founded in April 1963. List of directors * Masuo Fukuhara (1963.5.1 – 1969.3.31) * Kōsaku Yosida (1969. ...

, he was appointed there an associate professor. In 1988/1990 he introduced the theory of

mixed Hodge module In mathematics, mixed Hodge modules are the culmination of Hodge theory, mixed Hodge structures, intersection cohomology, and the decomposition theorem yielding a coherent framework for discussing variations of degenerating mixed Hodge structures ...

s, based on the theory of

D-module In mathematics, a ''D''-module is a module over a ring ''D'' of differential operators. The major interest of such ''D''-modules is as an approach to the theory of linear partial differential equations. Since around 1970, ''D''-module theory has be ...

s in algebraic analysis, the theory of

perverse sheaves The mathematical term perverse sheaves refers to a certain abelian category associated to a topological space ''X'', which may be a real or complex manifold, or a more general topologically stratified space, usually singular. This concept was int ...

, and the theory of variation of Hodge structures and

mixed Hodge structure In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the Cohomology#Cohomology of varieties, cohomology of general algebraic variety, algebraic varieties. It is a generalization of a Hodge structure, ...

s (introduced by

Pierre Deligne Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Pr ...

) in algebraic geometry. This led, among other things, to a generalization of the fundamental decomposition theorems of

Alexander Beilinson Alexander A. Beilinson (born 1957) is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1 ...

Joseph Bernstein Joseph Bernstein (sometimes spelled I. N. Bernshtein; he, יוס(י)ף נאומוביץ ברנשטיין; russian: Иосиф Наумович Бернштейн; born 18 April 1945) is a Soviet-born Israeli mathematician working at Tel Aviv Un ...

Deligne Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Pr ...

, and

Ofer Gabber Ofer Gabber (עופר גאבר; born May 16, 1958) is a mathematician working in algebraic geometry. Life In 1978 Gabber received a Ph.D. from Harvard University for the thesis ''Some theorems on Azumaya algebras,'' written under the supervi ...

about perverse sheaves in positive characteristic to characteristic 0. The theory of Hodge D-modules forms the starting point for the theory of the twistor D-modules developed by

Claude Sabbah Claude Sabbah (born 30 October 1954) is a French mathematician and researcher at École Polytechnique. Education Sabbah received his doctoral degree from Paris Diderot University in 1976 under the supervision of Lê Dũng Tráng. Selected pub ...

and Takurō Mochizuki, which lead to led to another generalization of the Beilinson–Bernstein–Deligne–Gabber theorem by Mochizuki. In 2006 Saito, with Nero Budur and Mircea Mustață, generalized the notion of a

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 to ...

(''aka'' b-function or b-polynomial) to an arbitrary variety. Saito's research deals with "applications of the theory of mixed Hodge modules to algebraic geometry, including the theories of singularities, algebraic cycles, characteristic classes, and so on." In 1990 he was an Invited Speaker with talk ''Mixed Hodge Modules and Applications'' at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

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 ...

. In 1991 he was awarded the Spring Prize of the

Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ja, 日本数学会) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized ...

Selected publications

* * (over 600 citations) * * * (over 600 citations) * *

References

{{DEFAULTSORT:Saito, Morihiko 1961 births Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians University of Tokyo alumni Kyoto University alumni Academic staff of Kyoto University