Appears in collections : Conference on Arithmetic Geometry in honor of Luc Illusie, Distinguished women in mathematics

Given a disc in the plane select any point in the disc and cut the disc by four lines through this point that are equally spaced. We obtain eight slices of the disc, each having angle π/4 at the point. The pizza theorem says that the alternating sum of the areas of these slices is equal to zero. I will talk about higher-dimensional versions of this theorem, where the lines are replaced by a Coxeter arrangement and the pizza by a ball (or a more general shape), and explain how this problem sheds light on the combinatorics that appear in the spectral description of the intersection cohomology of Shimura varieties. This is joint work with Richard Ehrenborg and Margaret Readdy.