# Representation theory of infinite-dimensional Lie algebras

**Project level: **PhD

Conformal field theory plays a fundamental role in string theory and in the description of phase transitions in statistical mechanics. The basic symmetries of a conformal field theory are generated by infinite-dimensional Lie algebras including the Virasoro algebra. The representation theory of these algebras is a vast and very active area of research in pure mathematics and mathematical physics. Although reducible yet indecomposable representations are of great importance in logarithmic conformal field theory, relatively little is known about them. This project will examine such representations of the Virasoro algebra, of the affine Kac-Moody algebras and of certain classes of so-called W-algebras.