#### Title

New Computational Techniques in FJRW Theory with Applications to Landau Ginzburg Mirror Symmetry

#### Abstract

Mirror symmetry is a phenomenon from physics that has inspired a lot of interesting mathematics. In the Landau-Ginzburg setting, we have two constructions, the A and B models, which are created based on a choice of an affine singularity with a group of symmetries. Both models are vector spaces equipped with multiplication and a pairing (making them Frobenius algebras), and they are also Frobenius manifolds. We give a result relating stabilization of singularities in classical singularity to its counterpart in the Landau-Ginzburg setting. The A model comes from so-called FJRW theory and can be de fined up to a full cohomological field theory. The structure of this model is determined by a generating function which requires the calculation of certain numbers, which we call correlators. In some cases the their values can be computed using known techniques. Often, there is no known method for finding their values. We give new computational methods for computing concave correlators, including a formula for concave genus-zero, four-point correlators and show how to extend these results to find other correlator values. In many cases these new methods give enough information to compute the A model structure up to the level of Frobenius manifold. We give the FJRW Frobenius manifold structure for various choices of singularities and groups.

#### Degree

PhD

#### College and Department

Physical and Mathematical Sciences; Mathematics

#### Rights

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

#### BYU ScholarsArchive Citation

Francis, Amanda, "New Computational Techniques in FJRW Theory with Applications to Landau Ginzburg Mirror Symmetry" (2012). *All Theses and Dissertations*. 3265.

http://scholarsarchive.byu.edu/etd/3265

#### Date Submitted

2012-06-14

#### Document Type

Dissertation

#### Handle

http://hdl.lib.byu.edu/1877/etd5364

#### Keywords

FJRW Theory, Moduli Space of Curves, Frobenius algebra, Frobenius manifold, cohomological eld theory, genus-g, k-point correlators