Mirror Symmetry for K3 surfaces and beyond

Mirror symmetry is an intriguing phenomenon stemming from physics. It essentially predicts that Calabi–Yau manifolds have a "mirror partner," and that certain structures on the Calabi–Yau are mirrored in certain other structures on the mirror. There are several mathematical constructions for mirror symmetry, depending on the context. For certain K3 surfaces, there are two particular versions of mirror symmetry that we will discuss. One stems from certain lattice polarizations of the K3 surfaces in question, and the other comes from the Landau–Ginzburg correspondence and what is known as Berglund–Huebsch–Krawitz mirror symmetry. We will discuss the setting in which both of these mirror symmetry constructions apply, and show that they do in fact agree. If time permits, we will discuss some consequences and implications for nonabelian Landau–Ginzburg models.