Vyacheslav Futorny "Algebras of differential operators on algebraic varieties."

We will give an introduction to a fast growing representation theory of Lie algebras of polynomial vector fields on algebraic varieties. First we discuss algebras (associative) of differential operators, in particular Weyl algebras, and then proceed to the discussion of Lie algebras of polynomial vector fields. We will focus on the cases of the torus, sphere and algebraic curves. At the end we will discuss the state of the art of the theory for general varieties.