Abstract by Kyle Niendorf
Building a Landau-Ginzburg Model for String Theory Physics
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). There are two approaches to the problem of modeling the B-model; one is a geometric approach whereas the other, of interest today, is via a Landau-Ginzburg model. The Landau-Ginzburg model produces a vector space---called the state space---which has a product structure, making it an algebra. Until recently, mathematicians have not known how to define the product. There are currently two propositions describing how to define the correct product. However, the validity of each proposition for the product has yet to be rigorously examined. In this talk we look at the first of theseproducts, exploring the construction of the state space, algebra structure, and finally a conjecture on the nature of both of the proposed models in comparison with each other.