Incoherent Eisenstein series on U(n,n) and arithmetic geometry

In this lecture, I will discuss the structure of the non-singular Fourier coefficients of
the derivative at the central critical point of incoherent Eisenstein series on U(n,n). 
In certain cases, these coefficients coincide with the arithmetic degrees of
0-cycles on moduli spaces of abelian varieties.  The proof of this relation depends
on p-adic uniformization and the determination of the structure of special cycles on
Rapoport-Zink spaces. 
This is joint work with Michael Rapoport.