Multiple Mirrors and Derived Categories
Mirror symmetry predicts that for a given Calabi-Yau manifold X, there is a "mirror" manifold Y such that the symplectic behavior of X is dual to the algebraic behavior of Y. Deforming the algebraic structure on X can lead to multiple mirror varieties Y. As an example, I will discuss a mirror construction due to Berglund-Hubsch-Krawitz. As it turns out, the different mirror varieties in the BHK construction can be considered "physically" equal. Namely, the derived categories of the two mirrors, which encode the physical properties of these algebraic varieties, are equivalent. This talk is based on joint work with T. Kelly.