| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
I studied applications of pseudo-holomorphic curve theory in symplectic geometry to the study of periodic orbits of Hamiltonian systems.
Main achievements are: (1). Computation of symplectic capacity of unit disk cotangent bundle of a Riemannian manifold with boundary via geometry of free loop space. As an application, a good estimate of the shortest length of periodic billiard trajectory was obtained. (2). Construction of chain-level algebraic structures in string topology, which conjecturally correspond to higher products in Floer homology of cotangent bundles. (3). Proof of C-infinity closing lemma for three-dimensional Reeb flows and two-dimensional Hamiltonian diffeomorphisms using embedded contact homology.
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