Abstract: 

Drinfeld modular schemes were introduced by Drinfeld in order to prove the Langlands reciprocity of the function field analogue. Compactifying these moduli spaces is one of key steps for realizing the Langlands correpsondence in their l-adic cohomologies.
Drinfeld constructed the compactification for rank 2 moduli spaces. Higher rank moduli spaces were constructed by Kapranov, Gekeler and Pink by different methods. In this talk we discuss the arithmetic Satake compacfications of Drinfeld moduli schemes of any rank. Applications to algebraic Drinfeld moduli forms are addressed. This is joint work with Urs Hartl from Muenster University.