| Budget Amount *help |
¥41,470,000 (Direct Cost: ¥31,900,000、Indirect Cost: ¥9,570,000)
Fiscal Year 2019: ¥8,190,000 (Direct Cost: ¥6,300,000、Indirect Cost: ¥1,890,000)
Fiscal Year 2018: ¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2017: ¥8,190,000 (Direct Cost: ¥6,300,000、Indirect Cost: ¥1,890,000)
Fiscal Year 2016: ¥7,670,000 (Direct Cost: ¥5,900,000、Indirect Cost: ¥1,770,000)
Fiscal Year 2015: ¥8,970,000 (Direct Cost: ¥6,900,000、Indirect Cost: ¥2,070,000)
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| Outline of Final Research Achievements |
The moduli space of pseudoholomorphic maps from a surface to a symplectic manifold provides us with an important and powerful method to investigate global symplectic geometry. Compared with the case when the domain surface has no boundary, it is much more difficult to study the case when it has boundary mapped to a Lagrangian submanifold. By this grant, we have established the foundation of the theory of virtual fundamental chain (including the case with boundary), based on the theory of Kuranishi structure, in order to develop the intersection theory on the moduli space. We apply the foundation to a geometric realization of A_{\infty} structure and the mirror symmetry conjecture. For example, we proved a certain version of the mirror symmetry conjecture for any compact toric manifolds, and obtained new results on the structure of Hamiltonian diffeomorphism groups of certain symplectic manifolds.
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