## 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.