# 31 - Vertex algebras, instanton counting and invariants of 3 and 4 dimensional manifolds, 2019

Top Global Course Special Lectures 2 ## Vertex algebras, instanton counting and invariants of 3 and 4 dimensional manifolds
July 22, 23, 24, 25 and 26, 2019 |

#### 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 opetator algebras and conformal fields theories.
Characters of representations of vertex algebras.Simplest case -minimal models for Virasoro algebra. Conformal blocks and modular functor.Consructions of vertex algebras by reduction or by exstensions.

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