Algebra and Geometry Seminar

Almost 30 years ago, Berglund and Hübsch proposed a version of Mirror Symmetry for quasihomogeneous potentials, which was later completed by Berglund and Henningson, and then again independently by Krawitz. This has come to be known as BHK mirror symmetry. Basically it says that to a Landau-Ginzburg pair (W,G) of a potential W and a group of symmetries G, we can relate its BHK mirror (W‘,G‘) by a simple rule. Remarkably, this simple rule predicts other instances of mirror symmetry, including the very first known example of mirror symmetry for the quintic threefold. Recently, we have discovered an extension of BHK mirror symmetry that allows for nonabelian symmetries of W, namely we can allow G to be a nonabelian group. In this presentation, we will discuss BHK mirror symmetry, its relation with other forms of mirror symmetry, and the extension of BHK mirror symmetry to nonabelian groups.