Junior Geometry and QFT Seminar

Our goal will be to define chiral algebras on curves as D-modules with an antisymmetric "chiral bracket" map satisfying a version of the Jacobi identity. Most of the talk will be on D-modules: their use is to apply the methods of sheaf theory and homological algebra to the study of systems of linear partial differential equations, which has since expanded to find use in geometric representation theory among other areas. We will define D-modules ex nihilo, followed by a discussion of their formal properties and some examples. Near the end we will discuss what chiral algebras are, and time permitting, their appearance in 2D conformal field theory. This is the first of three talks about chiral algebras.