Yuri Berest, Cornell University
In 1982, I. G. Macdonald published a series of beautiful combinatorial conjectures related to classical root systems (or equivalently, compact Lie groups). These conjectures were in the focus of research in representation theory and geometry for over 30 years. In the early 1990s,
B. Feigin and P. Hanlon proposed a homological refinement of the Macdonald conjectures (nowadays known as the strong Macdonald conjectures) that were studied by many mathematicians and eventually settled in 2008. In this talk, I will give a 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 A. C. Ramadoss and W.-K. Yeung.