Junior Geometry and QFT Seminar

The theory of D-modules provides a convenient, algebraic language for describing vector bundles with connection. In the setting of differential geometry, such connections can be used to define a notion of parallel transport on a vector bundle. In this talk, I will explain the notion of a "crystal". This will allow us to define an analog of parallel transport that makes sense in the world of algebraic geometry. I will then sketch a proof that crystals and D-modules are in fact the same thing.