Kyōji Saitō (齋藤恭司, Saitō Kyōji; born 25 December 1944) is a Japanese

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, specializing in algebraic geometry and complex analytic geometry.

Education and career

Saito received in 1971 his

promotion Promotion may refer to: Marketing * Promotion (marketing), one of the four marketing mix elements, comprising any type of marketing communication used to inform or persuade target audiences of the relative merits of a product, service, brand or i ...

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

from the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

under

Egbert Brieskorn Egbert Valentin Brieskorn (7 July 1936, in Rostock – 11 July 2013, in Bonn) was a German mathematician who introduced Brieskorn spheres and the Brieskorn–Grothendieck resolution. Education Brieskorn was born in 1936 as the son of a mill cons ...

, with thesis ''Quasihomogene isolierte Singularitäten von Hyperflächen'' (Quasihomogeneous isolated singularities of hypersurfaces). Saito is a professor at the

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 (196 ...

(RIMS) of Kyoto University. Saito's research deals with the interplay among Lie algebras,

reflection group In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent c ...

s (

Coxeter group In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean refle ...

s),

braid group A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing two or more strands of flexible material such as textile yarns, wire, or hair. The simplest and most common version is a flat, solid, three-strande ...

s, and singularities of

hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidea ...

s. From the 1980s, he did research on underlying symmetries of period integrals in complex hypersurfaces. Saito introduced higher-dimensional generalizations of

elliptic integral In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (). Their name originates from their originally arising in ...

s. These generalizations are integrals of "primitive forms", first considered in the study of the unfolding of isolated singularities of complex hypersurfaces, associated with infinite-dimensional Lie algebras. He also studied the corresponding new automorphic forms. The theory has a geometric connection to "flat structures" (now called "Saito Frobenius manifolds"),

mirror symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D ther ...

Frobenius manifold In the mathematical field of differential geometry, a Frobenius manifold, introduced by Dubrovin,B. Dubrovin: ''Geometry of 2D topological field theories.'' In: Springer LNM, 1620 (1996), pp. 120–348. is a flat Riemannian manifold with a cer ...

s, and Gromov–Witten theory in algebraic geometry and various topics in mathematical physics related to string theory. Saito supervised the thesis of 7 Ph.D. students at Kyoto University, including Hiroaki Terao and Masahiko Yoshinaga. He was an Invited Speaker with talk ''The limit element in the configuration algebra for a discrete group: a précis'' at the International Congress of Mathematicians 1990 in Kyoto. In 2011 he was awarded the Geometry 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

* * * * *as editor with and

Masaki Kashiwara 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, ''D''-module theory, Hodge theory, sheaf theory and represent ...

, Atsushi Matsuo, and Ikuo Satake
''Topological Field Theory, Primitive Forms and Related Topics''
Birkhäuser Verlag, Progress in Mathematics, 1998 *
''Primitive automorphic forms''
in

Björn Engquist Björn Engquist (also ''Bjorn Engquist''; born 2 June 1945 in Stockholm) has been a leading contributor in the areas of multiscale modeling and scientific computing, and a productive educator of applied mathematicians. Life He received his PhD ...

Wilfried Schmid Wilfried Schmid (born May 28, 1943) is a German-American mathematician who works in Hodge theory, representation theory, and automorphic forms. After graduating as valedictorian of Princeton University's class of 1964, Schmid earned his Ph.D. at ...

(eds.) ''Mathematics Unlimited - 2000 and beyond'', Springer Verlag 2001, pp. 1003–1018
''Around the theory of the general weight system: relations with singularity theory, the generalized Weyl group and its invariant theory, etc.''
in

Katsumi Nomizu was a Japanese-American mathematician known for his work in differential geometry. Life and career Nomizu was born in Osaka, Japan on the first day of December, 1924. He studied mathematics at Osaka University, graduating in 1947 with a Maste ...

''Selected papers on harmonic analysis, groups and invariants'', AMS Translations, Series 2, vol. 183, 1991 *as editor with

Bernard Teissier Bernard Teissier (; born 1945) is a French mathematician and a member of the Nicolas Bourbaki group. He has made major contributions to algebraic geometry and commutative algebra, specifically to singularity theory, multiplicity theory and va ...

and Lê Dũng Tráng: ''Singularity Theory'', World Scientific 1995 *

References

External links

Kyoji Saito, Research Institute for Mathematical Sciences, Kyoto University
{{DEFAULTSORT:Saito, Kyoji 20th-century Japanese mathematicians 21st-century Japanese mathematicians University of Göttingen alumni Academic staff of Kyoto University 1944 births Living people Algebraic geometers