Factorization Algebras

Prerequisites:: Algebraic Geometry I and II: sheaves, cohomology of sheaves, étale topology. Lie algebras: simple finite dimensional algebras, affine Kac-Moody Lie algebras.

It would also be useful to know vertex algebras: these will be defined in class but main theorems will not be proved.

We will study chiral and factorization algebras from Beilinson and Drinfeld. Ran Space. D-modules. Quasi-coherent sheaves on the Ran space. Factorization. Affine Grassmanian. Beilinson and Drinfeld Grassmanian. Factorizing line bundles. Factorization algebras. Units. Connections. Chiral algebras. Chiral homology. Vertex algebras. Relations with chiral algebras. 

References:
A. Beilinson and V. Drinfeld. – Chiral algebras. 51 of Colloquium Publications. AMS 2004. 
E. Frenkel and D. Ben-Zvi. – Vertex algebras and Algebraic curves. 88 of Mathematical surveys and monographs. Second edition. AMS 2004.

* Standard program. The teacher has the autonomy to make any changes