Homological Mirror Symmetry for a Calabi-Yau Hypersurface in Projective Space

Joint IAS-PU Symplectic Geometry Seminar
Topic:Homological Mirror Symmetry for a Calabi-Yau Hypersurface in Projective Space
Speaker:Nicholas Sheridan
Affiliation:Princeton University; Member, School of Mathematics
Date:Friday, October 12
Time/Room:4:30pm - 5:30pm/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.