Interaction between Geometry and various mathematics

点击翻译按钮获取中文摘要

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.