Abstract :

In 1982, I. G. Macdonald conjectured a series of combinatorial identities related to root systems. These beautiful conjectures were in the focus of research in representation theory for over 30 years. In the late 80's/early 90s, Feigin and Hanlon proposed a homological generalization of the Macdonald conjectures (known as the strong Macdonald conjectures) that were studied by a number of mathematicians and eventually proved in 2008. In this talk, I shall discuss a natural topological interpretation of the strong Macdonald conjectures and discuss a related conjecture that remains wide open. The talk is based on joint work with Yuri Berest and Wai-Kit Yeung.