A Landau--Ginzburg model of Borcea--Voisin mirror symmetry

In recent years there has been much activity investigating a certain mirror symmetry construction for Landau--Ginzburg models as described by Berglund--Hübsch, and later modified by Krawitz and Berglund--Henningson. On the other hand, Borcea and Voisin described a particular version of mirror symmetry involving the quotient of the product of a K3 surface and an elliptic curve. This is often referred to as Borcea--Voisin mirror symmetry. In this talk I will compare Borcea--Voisin mirror symmetry with Berglund--Hübsch mirror symmetry, and show that they do not agree. Instead we will consider a new version of mirror symmetry for particular Landau--Ginzburg models that is inspired by Borcea--Voisin mirror symmetry.