Topology, its Applications to Mathematical Physics and Numerical Computations

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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.