Mathematics on Manifolds.

1.首席研究员和其他研究员在其他数学家的合作下，就流形上的各自主题进行了研究。2.我们组织并举办了以下专题讨论会，结果证明是有价值的：（1）霍奇结构，时期地图和Torelli问题（第一和第三年）研讨会。(2)解析簇及其奇异性专题讨论会（第一年）。(3)算术代数几何概要（第一年）。(4)代数几何专题讨论会（第一和第二年）。(5)Painleve方程研讨会（第一年）。(6)微分几何与复微分几何专题讨论会（第二年）。(7)几何与自守形式专题讨论会（第二年）。(8)Dynkin数学研讨会（第三年）。(9)数学物理与代数几何专题讨论会（第二年）。(10)交换代数研讨会（第一，第二和第三年）。(11)研讨会上半群（第一，第二和第三年）。3.我们派遣了几位数学家参加与我们的兴趣密切相关的其他数学领域的研讨会。首席研究员和其他研究员亲自或通过担架相互沟通，收集关于可能有趣和重要的专题讨论会主题的信息，我们印刷和分发了专题讨论会和讲习班的会议记录。

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.