| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
Mirror symmetry is a symmetry which interchanges the role of the symplectic geometry and complex algebraic geometry. The purpose of this reserch is a trial for a deep understanding of the non-commutative Hodge theory in the theorey of the mirror symmetry and for a solution to important problems in related areas.
The following are examples of our research results. Motivated by the non-commutative Hodge theory for categories of matrix factorizations, we proposed a set of axioms for orbifold Jacobian algebras, and we proved the existence and the uniqueness of them. We have also been studying the entropy of endo-functors on derived categories of coherent sheaves on smooth projective varieties and show the Gromov-Yomdin type theorem for some varieties.
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