| Budget Amount *help |
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2020: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2019: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Outline of Final Research Achievements |
We study theory and applications of cluster algebras which is one of algebraic and combinatorial structure in integrable systems. We obtain the following new results and insights: derivation of dilogarithm identities in cluster algebras by classical mechanical method, systematic proofs of synchronicity phenomenon and related conjectures, derivation of the relation between cluster algebra theory and scattering diagrams in the cluster algebraic point of view, proof that any consistency relation in a cluster scattering diagram is generated by the pentagon identity among dilogarithm elements, dilogarithm identities associated to cluster scattering diagrams and their quantizations, derivation of product formula of F-polynomials.
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