Topology, its Applications to Mathematical Physics and Numerical Computations

K.Yamaguchi的主要目的是从调和映射的角度研究最近得到很好研究的标记位形空间的拓扑，并研究几种映射空间的拓扑。前者的研究主要基于与m.g estat（美国罗切斯特大学）和a.c ozlowski（富山国际大学）的合作。首先，我们考虑了由所有d次单复多项式组成的空间SP^d_n(C)的同伦类型，并显式地确定了它。接下来，他研究了它的泛化，这与著名的Gromov的small - hirsh原理有关。特别是，他找到了一些典型的例子，并发表了结果。此外，他和a .科兹洛夫斯基发现了它与瓦西里耶夫最近的工作的关系，并提交了关于这项工作的预印本。最后，关于后一个主题，他注意到了SO(4)的自同伦等价群的群结构，并提交了它。三泽先生从偏微分方程的角度研究了与调和映射有关的求值原理。特别是，他发现了p调和映射及其梯度流的存在性和正则性，论文很快发表。M.Fukuhara考虑了区域分解及其在数值计算中的应用。

The main purpose of K.Yamaguchi is to study the topologies of labelled configuration spaces, which are recently well studied from the point of view of harmonic maps and is to investigate the topologies of several mapping spaces. The former study is mainly based on the joint work with M.Guest (Univ. Rochester, USA) and with A.Kozlowski (Toyama Internaitinal Univ.). First, recently we considered the homotopy type of the space SP^d_n(C) consisting of all monic complex polynomials of degree d and determined it explicitely. Next, he investigated its generalization, which is related to well-known Gromov's Smale-Hirsh principle. In particular1 he found some typical examples of it and published its result. Moreover, he and A.Kozlowski found its relations to the recent work of Vassiliev and submitted the preprint with respect to this work. Finally, concerning to the latter subject, he noticed the group structure of the group of self-homotopy equivalences of SO(4) and submitted it. M.Misawa studied the valation principle related to harmonic maps from the point of view of partial differential equation. In particular, he found the existence and regurality of p-harmonic maps and its gradient flows, whose paper is soon appeared. M.Fukuhara considered the domain decomposition and its applications to numerical computations.