Affine Lie algebras and the Rogers-Ramanujan identities

The famous Weyl-Kac formula gives an inclusion-exclusion type expression for the characters of integrable highest weight modules of affine Kac-Moody algebras. In this talk I will describe alternative character formulas that are combinatorial in nature. I will then show how these new formulas give rise to far-reaching generalisations of the celebrated Rogers-Ramanujan identities.