SEEKING FURTHER POSSIBILITIES OF MATHEMATICS

通过本课题的研究，我们在以下领域取得了丰硕的成果：(1)实分析方法在非线性演化方程中的应用(2)类型与证明理论(3)锥流形与双曲几何(4)超平面构型的数学排列(5)椭圆型和抛物型偏微分方程中的集中现象(6)反问题的数学理论及其数值分析。详细的报告（或讲稿）已安排由日本数学学会出版。我们的项目确实对许多领域做出了贡献，这符合我们最初的目标，首先，鼓励非传统的数学挑战，促进小组研究会议（区域研讨会或RW’s），其次，从而确保相关活动。

Through the present research project, we have obtained fruitful results in the following fields :(1) Applications of methods of real analysis to non-linear evolution equation(2) Theories of types and proofs(3) Cone manifolds and hyperbolic geometry(4) Mathematical arrangements of hyperplanes configurations(5) Concentration phenomena in elliptic and parabolic partial differential equations(6) Mathematical theory of inverse problems and their numerical analysis.Detailed reports (or lecture notes) have been arranged to be published by the Mathematical Society of Japan. That our project did contribute to so many fields conforms to our original objective, firstly, to encourage non-conventional mathematical challenges, promoting small group research sessions (Regional Workshops or RW's), and secondly, thus to assure relevant activities.