Homological Mirror Symmetry for a Calabi-Yau hypersurface in projective space

Homological Mirror Symmetry for a Calabi-Yau hypersurface in projective space

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Nick Sheridan, Princeton University and IAS
Fine Hall 322

We prove homological mirror symmetry for a smooth Calabi-Yau hypersurface in projective space. In the one-dimensional case, this is the elliptic curve, and our result is related to that of Polishchuk-Zaslow; in the two-dimensional case, it is the K3 quartic surface, and our result reproduces that of Seidel; and in the three-dimensional case, it is the quintic three-fold. After stating the result carefully, we will describe some of the techniques used in its proof, and draw lots of pictures in the one-dimensional case.