Japanese mathematician (born 1961)
Morihiko Saitō (斎藤 盛彦 , Saitō Morihiko , born 1961) is a Japanese mathematician, specializing in algebraic analysis and algebraic geometry .
Education and career
After graduating from Aiko High School in Matsuyama , Saito completed undergraduate study in mathematics at the University of Tokyo and in 1979 completed the master's program there. In 1986 he received his D.Sc. from Kyoto University . After working as a research assistant at Kyoto University's Research Institute for Mathematical Sciences , he was appointed there an associate professor.
In 1988/1990 he introduced the theory of mixed Hodge modules , based on the theory of D-modules in algebraic analysis, the theory of perverse sheaves , and the theory of variation of Hodge structures and mixed Hodge structures (introduced by Pierre Deligne ) in algebraic geometry. This led, among other things, to a generalization of the fundamental decomposition theorems of Alexander Beilinson , Joseph Bernstein , Deligne , and Ofer Gabber about perverse sheaves in positive characteristic to characteristic 0.[ 1] 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 , 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 (aka b-function or b-polynomial) to an arbitrary variety.[ 2]
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."[ 3]
In 1990 he was an Invited Speaker with talk Mixed Hodge Modules and Applications at the International Congress of Mathematicians in Kyoto . In 1991 he was awarded the Spring Prize of the Mathematical Society of Japan .[ 4]
Selected publications
"Hodge structure via filtered D-Modules" (PDF) . Astérisque . 179–180: 342–351. 1985.
Saito, Morihiko (1988). "Modules de Hodge polarisables" . Publ. RIMS, Kyoto Univ . 24 (6): 849–995. doi :10.2977/prims/1195173930 . (over 600 citations)
Saito, Morihiko (1989). "On the structure of Brieskorn lattice" . Annales de l'Institut Fourier . 39 (1): 27–72. doi :10.5802/aif.1157 .
"Introduction to mixed Hodge modules" (PDF) . Astérisque . 179–180: 145–162. 1989; in Actes du Colloque de théorie de Hodge, Luminy, 1–6 Juin 1987 {{cite journal }}
: CS1 maint: postscript (link )
Saito, Morihiko (1990). "Mixed Hodge modules" . Publ. RIMS, Kyoto Univ . 26 (2): 221–333. doi :10.2977/prims/1195171082 . (over 600 citations)
Saito, Morihiko (1990). "Decomposition theorem for proper Kähler morphisms" . Tohoku Mathematical Journal . Second Series. 42 (2): 127–148. doi :10.2748/tmj/1178227650 . MR 1053945 .
Budur, Nero; Saito, Morihiko (2005). "Multiplier ideals, V-filtration, and spectrum". Journal of Algebraic Geometry . 14 (2): 269–282. arXiv :math/0305118 . doi :10.1090/S1056-3911-04-00398-4 . MR 2123230 . S2CID 11520237 .
References
International National Academics