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 microfunctio ...

and

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

Education and career

After graduating from Aiko High School in

Matsuyama file:Matsuyama city office Ehime prefecture Japan.jpg, 270px, Matsuyama City Hall file:Ehimekencho-20040417.JPG, 270px, Ehime Prefectural Capital Building is the capital Cities of Japan, city of Ehime Prefecture on the island of Shikoku in Japan ...

, 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 = National university, Public (National) , endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff ...

. 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 t ...

s, based on the theory of

D-module In mathematics, a ''D''-module is a module (mathematics), module over a ring (mathematics), ring ''D'' of differential operators. The major interest of such ''D''-modules is as an approach to the theory of linear partial differential equations. Sin ...

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 intro ...

, and the theory of

variation of Hodge structures In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold. Hodge structures ...

and

mixed Hodge structure In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the cohomology of general algebraic varieties. It is a generalization of a Hodge structure, which is used to study smooth projective varieties. I ...

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 Univ ...

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 and

Takurō Mochizuki Takurō Mochizuki (望月拓郎, born 28 August 1972) is a Japanese mathematician at Kyoto University. Overview As a student at the University of Kyoto in 1994, Mochizuki left his undergraduate studies early to become a graduate student in ma ...

, 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 Mircea Immanuel Mustață (; born 1971 in Romania) is a Romanian-American mathematician, specializing in algebraic geometry. Mustață received from the University of Bucharest a bachelor's degree in 1995 and a master's degree in 1996 and from the ...

, 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 ...

(''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 ci ...

. 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