TiTle:  W-algebras and the representation theory of affine Lie algebras

Abstract:  In this talk, I will explain how the BRST reduction functor connects affine Lie algebras and W-algebras. The vanishing property of BRST homology implies that this functor is exact from the category of integrable affine modules to the category of W-algebra modules, providing a powerful tool for computing characters of W-modules. I will also discuss how this vanishing property extends to larger categories, such as relaxed modules, and its implications for the broader representation theory of affine Lie algebras beyond the BGG or integrable settings.