NSF-CGP Science Fellowship Program: Research in Geometry and Topology

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9303037 Guest This award will support a cooperative research project between Professor Martin Guest, Department of Mathematics, University of Rochester, New York, and Professor Mutsuo Oka, Department of Mathematics, Tokyo Institute of Technology in Japan. Dr. Yoshihiro Ohnita of the Tokyo Metropolitan University and Dr. Mikio Furuta at Tokyo University will also participate in the project. During his twelve- month visit Professor Guest and his Japanese colleagues will continue their previous joint research on the topology of the space of harmonic maps of a Riemann surface into a Lie group. These maps are of interest from the point of view of traditional differential geometry and also from the point of view of gauge theories in mathematical physics. The researchers will study a systematical description of the singularities of complete intersection varieties and singularities of the mappings. A complete intersection variety will be interpreted as the regular fiber of a holomorphic mapping between affine or toric spaces. They will attempt to determine how the topology of regular fiber or singular fibers changes under a homotopy of a given mapping. Results of the research have probable application in advanced mathematics theories as well as various areas of physics such as theoretical atomic physics. Professor Guest is an accomplished mathematician who is currently one of several authorities working in the field of variational principles (harmonic maps) as applied to problems in mathematical physics, specifically solitons and gauge theory. Dr. Oka is an authority on toric varieties. Dr. Ohnita has expertise in the area of differential geometry, especially Lie groups and harmonic maps and Dr. Furuta's specialty is moduli spaces of Yang-Mills instantons. Japan is a world leader in the areas of toric varieties and infinite dimensional Lie algebras and integrable systems. Since the investiga- tor's previous collaboration proved to be very produ ctive in terms of new directions of research as well as in terms of publications it is anticipated that the proposed project will provide similar new scientific opportunities. This project is supported by the NSF-CGP (Center for Global Partnership) Science Fellowship Program. ***