2005 Fiscal Year Final Research Report Summary
Geometry and topology of integrable systems, with computer-aided experimentation and visualization
| Project/Area Number |
14204005
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
GUEST Martin Tokyo Metropolitan University, Faculty of Urban Liberal Arts, Professor, 都市教養学部, 教授 (10295470)
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| Co-Investigator(Kenkyū-buntansha) |
OHNITA Yoshihiro Osaka City University, Graduate School of Science, Professor, 理学研究科, 教授 (90183764)
MIYAOKA Reiko Kyushu University, Faculty of Mathematics, Professor, 数理学研究院, 教授 (70108182)
OTOFUJI Takashi Nihon University, College of Engineering, Lecture, 工学部, 講師 (70339266)
HAMADA Tatsuyoshi Fukuoka University, Faculty of Science, Assistant, 理学部, 助手 (90299537)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Geometry / Topology / Integrable systems / Quantum cohomology / Computer experiments / Visualization |
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| Research Abstract |
Research problems in geometry and topology were investigated using methods from the theory of integrable systems. These included research on the classification of constant mean curvature (CMC) surfaces, isoparametric manifolds, Lagrangian submanifolds, harmonic maps, and quantum cohomology. The principal investigator obtained results on the D-module structure of quantum cohomology, and began a systematic study of relations between quantum cohomology and integrable systems.
Computer experiments played an important role in this project. MAPLE was used for computations with differential operators and differential equations, 3D-XplorMath was used for lattice model simulations, and CMC-Lab was used to study CMC surfaces. Several domestic and international research conferences were supported or partially supported, concentrating on the theme of "geometry and visualization". New techniques of computer experimentation and visualization were introduced at these conferences by researchers from Germany and the USA.
Dissemination and promotion of such computer techniques in Japan was an important goal of this project. The Research Assistant and several investigators wrote Japanese documentation and demonstrated software at conferences. Two websites were developed as part of this project : "geom" (for the Geometry Section of the Mathematical Society of Japan), and "tmugs" (for geometry research activities in the Tokyo Metropolitan area). Three "computer tutorials" were held towards the end of the project period. These tutorials were based on experience gained during the project, and will serve as a model for future development of this research area and associated human resources in Japan.
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