#### Abstract

Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. We verify this conjecture for a wide class of singularities on the level of Frobenius algebras, generalizing work of Krawitz [10]. We also review the relevant parts of the constructions.

#### Degree

MS

#### College and Department

Physical and Mathematical Sciences; Mathematics

#### Rights

http://lib.byu.edu/about/copyright/

#### BYU ScholarsArchive Citation

Johnson, Jared Drew, "An Algebra Isomorphism for the Landau-Ginzburg Mirror Symmetry Conjecture" (2011). *All Theses and Dissertations*. 2793.

http://scholarsarchive.byu.edu/etd/2793

#### Date Submitted

2011-07-07

#### Document Type

Thesis

#### Handle

http://hdl.lib.byu.edu/1877/etd4594

#### Keywords

mirror symmetry, Landau-Ginzburg models, FJRW theory, mathematical physics, Frobenius algebra