Abstract by Kyle Niendorf
Mirror Symmetry B-model Construction Comparison
String Theory is currently receiving much attention mathematically. It predicts a phenomenon called Mirror Symmetry, which essentially exchanges complex structures on one model (the A-Model), for Kähler structures on another model (the B-model). The B-model has the structure of a Frobenius algebra, meaning it has a product and pairing satisfying certain properties. There are currently two propositions describing how to define the correct product on the B-model, one (BTW) defined axiomatically, and the other (He-Li-Li) defined using Hochschild cohomology. In order to reconcile these proposed models, we check the structure of the He-Li-Li model against the axioms of the BTW model. One of these axioms is of particular interest; in this talk we use the product structure of each model to construct a homomorphism of algebras in certain cases that will lead to a proof that this axiom is satisfied.