Introduction to Algebras of Chiral Differential Operators

Applications. Fedor MALIKOV

In these lectures we shall cover the following.

(1) Ordinary algebras of differential operators. Applications to representation theory.

(2) The Beilinson-Drinfeld categories: Lie* algebras, coisson algebras, chiral algebras. The purpose of this part will be to establish a link to the conventional vertex algebra theory.

(3) Algebras of chiral differential operators.

(4) Applications.