## 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

### Details

- Year/Term
- 2019 / Intensive, First semester

- Date
- July 22nd to July 26th, 2019

- Faculty/

Graduate School - Graduate School of Science

- Language
- English

- Instructor name
- Boris FEIGIN（Distinguished Visiting Professor,Kyoto University / Leading Researcher, Landau Institute for Theoretical Physics）

- Place
- 127 Conference Room, Faculty of Science Bldg No 3

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