Soon after Gromov’s applications of pseudo-holomorphic curves to symplectic topology, Floer invented an infinite-dimensional Morse theory by analyzing moduli spaces of pseudo-holomorphic curves to make substantial progress on Arnold’s conjecture. Now, Floer theory has been one of the most essential tools to study mirror symmetry as Fukaya category constructed from Floer theory serves as one side of the duality relation proposed by Kontsevich, called homological mirror symmetry conjecture. In this talk, we will review some aspects of developments of symplectic topology and mirror symmetry, and discuss current developments of Floer theory of partial flag varieties.
