mathematics

Kyoji Saito

Kyoji Saito is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Kyoji Saito rather than just read about it. In short: Kyōji Saitō (齋藤恭司, Saitō Kyōji; born 25 December 1944) is a Japanese mathematician, specializing in algebraic geometry and complex analytic geometry. Education and career 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).

Key takeaways

Kyoji Saito belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Kyoji Saito to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Kyoji Saito from memory before moving on to harder problems.

Reference excerpt

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

Education and career 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.

Selected publications Brieskorn, Egbert; Saito, Kyoji (1972). "Artin-Gruppen und Coxeter-Gruppen". Inventiones Mathematicae. 17 (4): 245–271. Bibcode:1972InMat..17..245B. doi:10.1007/BF01406235. MR 0323910. S2CID 120737658. Saito, Kyoji (1980). "Theory of logarithmic differential forms and logarithmic vector fields". J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (2): 265–291. hdl:2261/6265. MR 0586450. Saito, Kyoji (1982). "Primitive forms for a universal unfolding of a function with an isolated critical point". J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (3): 775–792. hdl:2261/6324. MR 0656053. Saito, Kyoji (1983). "Period mapping associated to a primitive form". Publ. Res. Inst. Math. Sci. 19 (3): 1231–1264. doi:10.2977/prims/1195182028. MR 0723468. as editor with and Masaki Kashiwara, Atsushi Matsuo, and Ikuo Satake: Topological Field Theory, Primitive Forms and Related Topics, Birkhäuser Verlag, Progress in Mathematics, 1998 Saito, Kyoji; Takahashi, Atsuki (2008), "From primitive forms to Frobenius manifolds", From Hodge theory to integrability and TQFT: tt*-geometry, Proceedings of Symposia in Pure Mathematics, vol. 78, American Mathematical Society, pp. 31–48, CiteSeerX 10.1.1.307.1944, doi:10.1090/pspum/078/2483747, ISBN 9780821844304, MR 2483747 {{citation}}: Cite uses deprecated parameter |citeseerx= (help) Primitive automorphic forms, in Björn Engquist, Wilfried Schmid (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 Selected papers on harmonic analysis, groups and invariants, AMS Translations, Series 2, vol. 183, 1991 as editor with Bernard Teissier and Lê Dũng Tráng: Singularity Theory, World Scientific 1995 Saito, Kyoji (2006). "Eta-product η ( 7 τ ) 7 / η ( τ ) {\displaystyle \eta (7\tau )^{7}/\eta (\tau )} ". arXiv:math/0602367.

References

External links Kyoji Saito, Research Institute for Mathematical Sciences, Kyoto University

Illustrations

Worked examples

Example 1 — a first encounter with Kyoji Saito

Start with the simplest possible case. Write down what Kyoji Saito claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kyoji Saito before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kyoji Saito ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kyoji Saito

In research: Kyoji Saito appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Kyoji Saito in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Kyoji Saito is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kyoji Saito outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Kyoji Saito in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kyoji Saito means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Kyoji Saito in simple terms?

Kyōji Saitō (齋藤恭司, Saitō Kyōji; born 25 December 1944) is a Japanese mathematician, specializing in algebraic geometry and complex analytic geometry. Education and career Saito received in 1971 his promotion Ph.D. from the University of Göttingen under Egbert Brieskorn, with thesis Quasihomogene i…

Why does Kyoji Saito matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kyoji Saito?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kyoji Saito.