| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We construct a completely integrable system on the Grassmannian of two-planes in an n-space associated with any trivalent tree with n leaves, and compute the potential function for its Lagrangian torus fiber by using its toric degeneration. The potential functions for different trees are related by a rational coordinate change, and the corresponding moment polytopes are related by its "tropicalization".
The Gelfand-Cetlin system has non-torus Lagrangian fibers on some of the boundary strata of the moment polytope. We compute Floer cohomologies of such non-torus Lagrangian fibers in the cases of the three-dimensional full flag manifold and the Grassmannian of two-planes in a four-space.
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