| Budget Amount *help |
¥3,210,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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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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