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

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Top Global Course Special Lectures 2

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

Boris Feigin
Kyoto University / Distinguished Visiting Professor
Landau Institute for Theoretical Physics / Leading researcher

July 22, 23, 24, 25 and 26, 2019
127 Conference Room Faculty of Science Bldg. #3, Kyoto University

Lecture Video

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