| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
Random plane partitions or melting crystal model was an old topic in the branch of combinatorics. However, it has been found surprising relations with other branches in modern mathematical physics, such as the Seiberg-Witten theory of supersymmetric gauge theories, Gromov-Witten's invariants and the mirror symmetry of Calabi-Yau 3-folds. The model has been also studied from the integrable system viewpoint. We further elucidate integrable structures of various melting crystal models, using quantum torus symmetry. It explains clearly the underlying integrable structure is Toda hierarchy and its cousins. Using the symmetry, we also derive the q-difference equations wave functions of topological branes probed in the tological vertex chains satisfy.
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