Notes on affine W-algebras

Abstract: These are expanded and revised notes for a minicourse entitled "Affine W-algebras", which took place as part of the thematic month "Quantum Symmetries" at the Centre de Recherches Mathematiques in Montreal, Canada in October 2022. The first few sections consist of rapid introductions to vertex algebras, affine Kac-Moody algebras and their integrable and admissible modules, and the homological BRST procedure for quantum Hamiltonian reduction. The affine W-algebras are defined using these ingredients. The remainder of the notes treats the structure and representation theory of the exceptional affine W-algebras, with emphasis on modular tensor categories of representations.