Interaction between Geometry and various mathematics

1995年：福谷和Y.Oh研究了余切丛上的亏格零开弦，并发现它等价于有理同伦理论。(This工作将由Asian J.Math.出版。福谷还研究了高等亏格的情况，发现它与Chern-Simons微扰理论有关。作为该基金的主要活动，我们举办了一个研讨会“无限群与几何”，并发表了250多页的报告。了解几何群论的最新发展对几何学家有很大的帮助。1996年：福谷与K.Ono证明了Arnold关于周期哈密顿系统的周期轨道数的猜想的同调版本。福谷等人还写了一篇关于无穷维范畴的同调代数及其在3维有边流形的Floer同调中的应用的论文，作为该资助的主要活动，福谷、古田等人在理论物理（特别是超对称规范理论和超弦理论）方面进行了一系列的讨论。基于这些研讨会，我们有一个研讨会在3月底对塞贝格维滕理论等，以提高数学家的理解物理规范理论，弦理论等，希望将其应用到未来的研究数学。我们还出版了250页的报告规范理论弦理论等这是为数不多的文章之一writtne数学家在这个问题上。

1995 : Fukaya with Y.Oh studied genus zero open string on the cotangent bundle and ind that it is equivalent to the rational homotopy theory. (This work will be published from Asian J.Math.)Fukaya also studied higher genus case and find that it is related to Chern-Simons perturbation theory.As a main activity based on this grant, we had a workshop "Infinite group and geometry" and publish a report over 250 pages. It helps a lot for geometers to know the recent development of geometric group theory.1996 : Fukaya with K.Ono proved a homology version of Arnold's conjecture on the number of periodic orbit of the periodic hamiltonian system. They also gave a construction of Gromov-Witten in variant for general symplectic manifolds.Fukaya also wrote a paper on the homological algebra of A infinity category and its application to the Floer homology of 3 manifolds with boundary.As a main activity based on this grant, Fukaya, Furuta etc have a series of seminars on theoretical physics, (especially supper symmetric gauge theory and supper string theory). Based on these seminars we had a workshop at the end of March on Seiberg Witten theory etc to improve mathematician's understanding of the physics of Gauge theory, String theory etc. hoping to apply it to the future research in Mathematics.We also published 250 pages of reports on Gauge theory String theory etc. This is one of a few article writtne by Mathematician on this subjects.