Abstract by Clara Huber
Construction of the Landau-Ginzburg Model
From String Theory, we are introduced to the idea of Mirror Symmetry, which predicts an isomorphism between the structures of the A-Model and the structures of B-Model. The B-Model should come equipped with a state space and a product making it a Frobenius Algebra, however, the product structure on the B-Model was not known mathematically until recently. In fact, within the last few years, two groups of mathematicians have proposed two seemingly different product structures on the B-model state space. One of the product structures is defined axiomatically while the other is defined using something called a Hochshild cohomology of some category. In this talk, we will discuss the relationship with the product and take an axiomatic approach towards showing in certain cases the two products define the same Frobenius Algebra.