Unitary Shimura varieties are moduli spaces of abelian
varieties with extra structure. Rapoport-Zink spaces (moduli spaces of
p-divisible groups with extra structure) are key tools in studying the
supersingular loci of these Shimura varieties. In this talk, we'll
discuss the geometry of the GL(4) Rapoport-Zink space. As an
application, we'll also discuss the geometry of the supersingular loci
of some particular unitary Shimura varieties.