USask PIMS Geometry and Physics (GAP) Seminar: Yuly Billig

AV-modules are representations of Lie algebra V of vector fields that admit a compatible action of the commutative algebra A of functions. This notion is a natural generalization of D-modules. In this talk we shall start by reviewing the theory of AV-modules over smooth irreducible affine varieties. When variety X is projective, it is necessary to consider sheaves of AV-modules. We describe associative algebras that control the category of AV-modules, and construct a functor from the category of strong representations of Lie algebra of jets of vector fields to the category of AV-modules. This talk is based on the joint work with Colin Ingalls, as well as the work of Emile Bouaziz and Henrique Rocha.