2009 Fiscal Year Final Research Report
Study on integrable systems with algebra geometrical method
| Project/Area Number |
19740231
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Suzuka University of Medical Science (2008-2009)
The University of Tokyo (2007) |
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Principal Investigator |
YAMAZAKI Rei (井上 玲) Suzuka University of Medical Science, 薬学部, 助教 (30431901)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 数理物理 / 可積分系 / 超離散化 / トロピカル幾何 / 代数幾何 / ヤコビ多様体 |
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| Research Abstract |
By using algebro geometrical method, we studied the finite-dimensional discrete / ultradiscrete integrable systems. We generalized the notion of algebraically completely integrability to that of tropical geometry and piecewise-linear map, and constructed the general solution to the ultradiscrete periodic Toda lattice. We also explicitly constructed the rational solution to the Mumford system. By applying cluster algebra and cluster category, we proved the periodicity of T-system and Y-system whose origin is in quantum integrable models.
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