In 1982, I. G. Macdonald made a series of conjectures related to classical root systems (or, equivalently, compact Lie groups). These beautiful conjectures were in the focus of research in representation theory, geometry and combinatorics for over 30 years. In the late 80's/early 90s, B. Feigin and P. Hanlon proposed a homological generalization of the Mac-donald conjectures (known as the strong Macdonald conjectures) that were eventually proved in 2008. In this talk I shall discuss a natural topological interpretation of the strong Macdonald conjectures and present a series of new conjectures suggested by topology that remain wide open. The talk is based on joint work with Yuri Berest and Wai-Kit Yeung.