2011 Fiscal Year Final Research Report
Geometry and visualization of integrable systems and applications to quantum field theory and neuroscience
| Project/Area Number |
22654010
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
MARTIN Guest 首都大学東京, 理工学研究科, 教授 (10295470)
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| Co-Investigator(Renkei-kenkyūsha) |
ROBERT Sinclair 沖縄科学技術大学院大学, 数理生物学ユニット, 教授 (50423744)
SAKAI Takashi 首都大学東京, 理工学研究科, 准教授 (30381445)
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| Project Period (FY) |
2010 – 2011
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| Keywords | 微分幾何 / 可積分系 |
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| Research Abstract |
Certain differential equations are studied from the point of view of geometry and the theory of integrable systems. The solution of such an equation can be simulated, and visualized, as the motion of a lattice of point masses with nonlinear interactions between neighbouring masses. An important example from quantum field theory is the tt*-Toda lattice, first studied by Cecotti and Vafa. Guest and Lin have obtained theoretical results on the existence of solutions, consistent with computer simulations. Other examples such as the Kuramoto lattice are being studied. Future applications, e. g. to the mathematical interpretation of synchronization, are anticipated.
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