Mirror symmetry for K3 surfaces

Nathan Priddis
Brigham Young University 
There are several mirror symmetry constructions in mathematics each in a different context, but all describing the same physical phenomenon. In this talk we will examine two of these constructions: one obtained using lattice polarization of K3 surfaces, and the other using Berglund-Hübsch mirror symmetry for Landau-Ginzburg models. The main question we will address is: when both constructions apply do they agree? To answer this question, we will employ techniques from the theory of even lattices and primitive embeddings into the Picard lattice of the K3 surfaces. We will also discuss a few implications of this result to Calabi-Yau threefolds and to the computation of invariant lattices on K3 surfaces.