| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We have studied knot invariants and integrable difference equations by applying cluster algebras. We realized the braid group using cluster mutations on a punctured disk, and clarified the relation with Kashaev's R-matrix via quantum cluster algebra. We studied the symplectic structure for the difference equations associated with exchange matrices of period one. We introduced a generalization of the discrete Toda lattice equation by using the network model on a torus, and solved its initial value problem using algebraic geometry and combinatorics. Further, we constructed the symmetric group action on a quiver on a cylinder, and studied the geometric R-matrix of A-type from the view point of cluster algebra.
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