Solomon's descent algebra and hyperplane arrangements

In 1976, Solomon discovered a surprising subalgebra of the group algebra of a Coxeter group. This subalgebra—henceforth Solomon's descent algebra—is spanned by sums of elements with the same (Coxeter) descent set. In this talk, I will describe a beautiful connection, due to Bidigare, between Solomon's descent algebra and the world of hyperplane arrangements.