Mathematics on Manifolds.

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1. The head investigator and the other investigators carried out research on respective themes on manifolds with the cooperation of other mathematicians.2. We organized and held the following symposia on the themes which turned out to be worthwhile: (1) Workshops on Hodge srtuctures, period maps and the Torelli problen (the first and the third years). (2) symposium on analytic varieties and their singularities (the first year). (3) Symopsium on arithmetic algebraic geometry (the first year). (4) Algebraic geometry symposia (the first and the second year). (5) Symposium on the Painleve equations (the first year). (6) Symposia on differential geometry and complex differential gemetry (the second year). (7) Symposium on geometry and automorphic forms (the second year). (8) Symposium on Dynkin mathematics (the third year). (9) Symposium on mathematical physics and algebraic geometry (the second year). (10) Symposia on commutative algebra (the first, second and third years). (11) Symposia on semigroups (the first, second and third year).3. We dispatched several mathmaticians to symposia in other fields in mathematics which are closely related to our interest.4. The head investigator and the other investigators communicated with each other in person or by litters to collect information on possible themes of symposia which might be interesting and important.We printed and distributed the proceedings of the symposia and workshops.