Vertex algebras, instanton counting and invariants of 3 and 4 dimensional manifolds

Lecture 1 Boris FEIGIN

Course Description
1. Representation theory. Affine Kac-Moody algebras. Integrable representations. Characters formulas. Two ways to understand characters – geometric and combinatorial. Lefschetz fix points formula and Brion theorem.
2. Vertex operator algebras and conformal fields theories. Characters of representations of vertex algebras.Simplest case -minimal models for Virasoro algebra. Conformal blocks and modular functor. Constructions of vertex algebras by reduction or by extensions.
3. Elements of geometric representation theory. Vertex algebras and invariants of 4-dimensional manifolds.Instanton counting.
4. 3-dimensional manifolds and logarithmic theories. Invariants of 3-dimensional manifolds