The classical Pizza Theorem states that you can divide a disc (pizza)
fairly between two people by cutting it with four equidistributed
lines through an arbitrary point in the disc and then alternate the
slices. The higher dimensional Pizza Theorem is an extension to a
large class of Coxeter arrangements. We will outline a dissection
proof of this result. The main ingredient of the proof is the notion
of 2-structures, a class of subarrangements introduced by Herb to
study discrete series characters of real reduced groups. As a
consequence the higher dimensional Pizza Theorem continues to hold
when replacing volume with the intrinsic volumes.
This is joint work with Sophie Morel and Margaret Readdy.