Mathematics on Manifolds.

1.首席调查员和其他调查员在其他数学家的合作下，对流形上的各自主题进行了研究。我们组织并举办了以下专题讨论会，结果证明这些专题是有价值的：(1)关于霍奇结构、时期地图和托雷利问题(第一年和第三年)的讲习班。(2)分析变种及其奇点研讨会(第一年)。(3)算术代数几何论著(第一年)。(4)代数几何专题讨论会(第一、二年级)。(5)Painleve方程研讨会(第一年)。(6)微分几何与复微分几何研讨会(第二年)。(7)几何与自同构形研讨会(第二年)。(8)动态数学学术讨论会(第三届)。(9)数学物理与代数几何学术研讨会(第二届)。(10)交换代数座谈会(一、二、三年)。(11)半群专题讨论会(第一、二、三年)。我们派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座谈会。首席调查员和其他调查员以面对面或小规模的方式相互交流，以收集可能有趣和重要的研讨会主题的信息。我们印刷并分发了研讨会和研讨会的记录。

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.