Supersingular Loci of Some Unitary Shimura Varieties

 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.