Hebrew University topology and geometry seminar

Abstract: Mirror symmetry is a phenomenon whereby Calabi-Yau manifolds come in pairs such that the symplectic geometry of the one is encoded in the complex geometry of the other. A heuristic framework for understanding this phenomenon is given by the SYZ conjecture, according to which the mirror is to be constructed as a moduli space of Lagrangian submanifolds of the original manifold augmented by some additional data. This is to a large extent made rigorous in Fukaya's theory of Lagrangian intersection Floer homology. If the mirror happens to be affine, it can alternatively be constructed as the spectrum of symplectic cohomology. I will discuss these two points of view in the setting of toric Calabi-Yau manifolds.