Floor homology, singularities and deformation theory

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We studied Floer theory in symplectic geometry in both theoretical foundation and applications. We extend Floer theory for Hamiltonian systems to that for Lagrangian intersections. Namely, we introduce the nation of filtered A_∞-algebras, filtered A_∞-bimodule etc. and give geometric constructions. As applications, we studied non-triviality of the Maslov class of Lagrangian embeddings, Lagrangian intersection under Hamiltonian deformations, etc. We also prove the flux conjecture using Floer theory for symplectomosphisms. This conjecture is basic for understanding how the group of Hamiltonian diffeomorphisms in the group of symplectomosphisms. These results are written up as research papers, preprints during the term of project.With Ohta, we tried to understand isolated singularities on complex surfaces through symplectic fillings of their links. In particular, we established uniquener of minimal symplectic fillings and studied its relation to Brieskorn's results for simple singularities. In the case of simple-elliptic singularities, we gave classification and interpreted Pinkham's result concerning the condition for existence of smoothings.These results are published in research journals.