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Abstract

Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted A and B ) that are constructed from a nondegenerate quasihomogeneous polynomial W and a related group of symmetries G . Duality between A and B models has been conjectured for particular choices of W and G . These conjectures have been proven in many instances where W is restricted to having the same number of monomials as variables (called \invertible). Some conjectures have been made regarding isomorphisms between A and B models when W is allowed to have more monomials than variables. In this paper we show these conjectures are false; that is, the conjectured isomorphisms do not exist. Insight into this problem will not only generate new results for Landau-Ginzburg mirror symmetry, but will also be interesting from a purely algebraic standpoint as a result about groups acting on graded algebras.

Author Bio

Nathan Cordner graduated with an undergraduate degree in mathematics from Brigham Young University in August 2014, and is currently a candidate for the Masters of Science degree in mathematics at BYU. He began researching with his mentor Dr. Tyler Jarvis in Algebraic Geometry and Mirror Symmetry in January 2013. Outside of academics, Nathan enjoys reading, hiking in the mountains, and playing various instruments such as the piano and the french horn.

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