FJRW Quantum Singularity Theory and the Landau Ginzburg Mirror Symmetry Conjecture
Amanda Francis, Brigham Young University

Mirror symmetry is a phenomenon from physics that has inspired a lot of interesting mathematics. One manifestation of mirror symmetry is in the Landau-Ginzburg setting. Here, we have two constructions that we can associate to an affine singularity and group of symmetries. These are the FJRW ring and the orbifold Milnor ring. Both are Frobenius algebras. It is conjectured that for a certain class of singularities each singularity and admissible group have a transpose singularity and transpose group so that the orbifold Milnor ring of one is isomorphic to the FJRW ring of the other. In this poster I will demonstrate what parts of the conjecture has already been verified, and use an example to demonstrate the mirror map.