Kyoji Saito

Kyōji Saitō (齋藤 恭司, Saitō Kyōji; born 25 December 1944) is a Japanese mathematician, specializing in algebraic geometry and complex analytic geometry.

Saito received in 1971 his promotion Ph.D. from the University of Göttingen under Egbert Brieskorn, with thesis Quasihomogene isolierte Singularitäten von Hyperflächen (Quasihomogeneous isolated singularities of hypersurfaces).

Saito is a professor at the Research Institute for Mathematical Sciences (RIMS) of Kyoto University.

Saito's research deals with the interplay among Lie algebras, reflection groups (Coxeter groups), braid groups, and singularities of hypersurfaces.

From the 1980s, he did research on underlying symmetries of period integrals in complex hypersurfaces.

Saito introduced higher-dimensional generalizations of elliptic integrals.

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, Frobenius manifolds, 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.