We construct eigenvarieties for unitary groups \(GU(r,s)\) that parametrise systems of eigenvalues of \(p\)-adic automorphic forms including Eisenstein series! The cuspidal locus of our eigenvarieties is strictly contained in the Eigenvarieties constructed by Andreatta, Iovita, and Pilloni.
We end this talk by giving some applications on p-adic L-functions.