École
de physique des Houches
E Frenkel
Vertex algebras and Algebraic Curves
Abstract:
Vertex algebras are algebraic objects that formalize the concepts of vertex
operators and operator product expansion from two-dimensional conformal field
theory. In this lectures we will give the definition of vertex algebra and
consider some examples. We will then give a coordinate independent description
of the vertex operators. This will allow us to define the spaces of
coinvariants and conformal blocks for a general vertex algebra and an
arbitrary pointed algebraic curve. When the complex structure of the curve and
other geometric data are varied, these spaces combine into a sheaf on the
relevant moduli space. From this perspective, vertex algebras appear as the
algebraic objects that encode the geometric structure of various moduli spaces
associated with algebraic curves.
lecture: