Conformal blocks in algebraic geometry

Abstract: These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe their fundamental properties -- such as factorization and sewing -- which imply that conformal blocks define vector bundles on moduli spaces of curves whose ranks and Chern classes can be computed explicitly. The second aim is to describe how line bundles on moduli of principal bundles over a curve -- and their sections -- can be understood via (twisted) conformal blocks for (twisted) affine Lie algebras.