Mathematics Colloquium

The Ramanujan identities are a famous pair of q-series identities first discovered by Rogers in 1894 and later rediscovered by Ramanujan. The identities have interpretations in terms of partition theory, the representation theory of infinite dimensional Lie algebras and knot theory. I will briefly describe some of the early history of the Rogers-Ramanujan identities and discuss some of the arithmetic questions that arose from them. I will then try to explain how the Rogers-Ramanujan identities may be generalised to almost all affine Lie algebras.