| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
We studied Gromov-Witten theory through global mirror symmetry. More concretely, (1) we proved a mirror theorem for complete intersections in toric orbifolds with Coates, Corti and Tseng; (2) we proved the crepant transformation conjecture for these spaces and showed that it is related to equivalences between derived categories of coherent sheaves with Coates and Jiang; (3) we constructed a theory of Fock sheaves for higher genus theory and showed a certain modularity of the potential with Coates; (4) we formulated Gamma conjecture for Fano manifolds with Galkin and Golyshev. We also obtained results on quantum K-theory, quantum Serre duality and a relationship between extremal transitions and quantum cohomology.
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