| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The melting crystal model, 4D and 5D supersymmetric gauge theory and topological string theory on local toric Calabi-Yau manifolds have a common feature that the partition functions can be formulated in the language of Young diagrams.
We found that the KP hierarchy, the Toda hierarhy and their reductions underlie these models of mathematical physics and their variants. In the course of this research, new computational techniques based on the quantum torus algebra and the quantum diloarithmic functions were also developed. Moreover, we derived the quantum mirror (or spectral) curves associated with these models from the integrable structures, and pointed out that they are analogues of the Kac-Schwarz operators that have been known in the theory of integrable hierarchies.
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