Parole chiave

**Abstract** There is a quantum singularity theory developed by Fan, Jarvis, and Ruan that produces a theory similar to Gromov-Witten theory, but from the input of a potential function and a group of symmetries. This can be considered as a Landau-Ginzburg A-model. There is also a Landau-Ginzburg B-model that can be constructed from similar input of a potential function and a group of symmetries. Finally, there is a construction of Berglund-Hübsch and Krawitz that links the two, and this is known as BHK mirror symmetry. However, this only works when the group of symmetries is abelian. Recently there have been generalizations of both the A-model and the B-model to include nonabelian groups of symmetries. In this talk we will review the previously mentioned theories, and I will describe an extension to BHK mirror symmetry that is conjectured to give an isomorphism between the LG A-model and the LG B-model for nonabelian groups of symmetries. I will describe a result giving an isomorphism between the state spaces for the LG A-model and the LG B-model.