Spectral and scattering theory for many particles Schrodinger operators

我们每一个研究者都从自己的角度对这个项目进行了研究，我们得到了以下结果。Yamagishi对在给定的一组位置之外非分歧的数域的极大prop-p-扩张（ρ是一个固定素数）的伽罗瓦群进行了研究。特别地，他研究了伽罗瓦群的生成元和关系的表示，以及进一步的上同调维数。Ohyama证明了：给定任意纽结n和任意自然数n，存在无穷多个解纽结数为1，其Vassiliev不变量的阶小于或等于n与n的Vassiliev不变量的阶重合. Fuchihe利用Vassiliev不变量的网图的代数性质对上述结果给出了另一个证明。Minami得到了一些结果，这些结果可以很容易地导出关于霍普金斯色分裂猜想的一个定理。并以图解的形式说明了M.韩国国立全南大学明奎郭教授，H。作为研究的一部分，岩下召开了一次国际会议，1999年7月在光州举行的第四次微分方程研讨会。来自韩国、台湾和日本的与会者进行了精彩的演讲和热烈的讨论，使会议取得了圆满成功。研讨会的主题涵盖了广泛的领域;薛定谔算子的谱和散射理论，线性和非线性波动方程解的可解性和渐近行为，算子，非线性椭圆方程的可解性，反问题等。岩下编辑并出版了研讨会的会议记录，这些会议记录也被分发给相关领域的许多数学家和一些外国大学的图书馆。

Each of us, the investigators has researched the project from his own point of view and we have obtained the following results.M. Yamagishi has given a survey on the Galois group of the maximal prop-p-extension (ρ a fixed prime) of a number field unramified outside a given set of places. Particulary, he has studied the presentation in terms of generators and relations, and further cohomological dimension of the Galois group.Y. Ohyama has proved that given any knot Κ and any natural number n, there exist infinite number of knots with unknotting number one whose Vassiliev invarinats of order less than or equal to n coincide with those of Κ. Futhermore he has given another proof to the result above by using an algebraic property of the web diagrams for Vassiliev invariants.N. Minami has obtained some result which can easily derive a theorem comcerning Hopkins' chromatic splitting conjecture. He also shows as diagram to give a note on the possibility of improving the divisibility of Seiberg-Witten invariant by Prof. M. Furuta.With Prof. Minkyu Kwak Chonnam National University, Korea, H. Iwashita held, as a part of the research, an international meeting, the Fourth Workshop on Differential Equations at Kwangju, July of 1999. The participants were from Korea, Taiwan and Japan and their lectures and heated discussions brought great success to the meeting. The subjects of the workshop covered a wide range of fields ; spectral and scattering theory for Schrodinger operators, solvability ad asymptotic behavior of solutions to linear and nonlinear wave equations, ators, solvability of nonlinear eliptic equations, inverse problems etc. H. Iwashita edited and published the proceedings for the workshop which were also delivered to many mathematicians in the ralated fields and libraries of some foreign universities.