| Budget Amount *help |
¥13,650,000 (Direct Cost: ¥10,500,000、Indirect Cost: ¥3,150,000)
Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2016: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2015: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Outline of Final Research Achievements |
We tried to extend the Katz theory for ordinary differential equations to higher dimensional case, and applied it to the global analysis of integrable systems. Here global analysis means the description of the monodromy, the connection problem and the description of the Stokes multipliers for irregular singular case. For KZ type equation, which comes from mathematical physics and plays an important role, we succeeded to define the multiplicative middle convolution, and gave an effective way to construct monodromy recursively. We also formulated the connection problem in higher dimensional case in a natural way. For integrable systems with irregular singularities, we gave effective methods to compute the asymptotic behaviors and Stokes multipliers.
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