Abstract

Mirror symmetry has been a significant area of research for geometry and physics for over two decades. Berglund and Hubsch proposed that for a certain family of singularities W, the so called "transposed" singularity WT should be the mirror partner of W. cite{BH} The techniques for constructing the orbifold LG models to test this conjecture were developed by FJR in cite{FJR} with a cohomological field theory generalized from the study of r-spin curves. The duality of LG A- and B-models became more elaborate when Krawitz cite{Krawitz} generalized the Intriligator-Vafa orbifold B-model to include contributions from more than one sector.This thesis presents a program written in Maple for explicitly computing bases for both LG A- and B-model rings, as well as the correlators for A-models to the extent of current knowledge. Included is a list of observations and conjectures drawn from computations done in the program.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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