Mirror symmetry is discovered by string theorists more than two decades ago. Mathematically, it predicts that the symplectic (resp. complex) geometry of a space is equivalent to the complex (resp. symplectic) geometry of another space. The two spaces are then said to form a mirror pair. My research to date is primarily concerned with the study of the Strominger-Yau-Zaslow (SYZ) conjecture which asserts that a mirror pair should admit dual special Lagrangian torus fibrations, and the interchange of geometric structures should be realized by certain Fourier-type transformations. Morally speaking, this means that mirror symmetry is nothing but a Fourier transform.
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