Motivated by questions arising in Hodge theory and the study of moduli spaces of algebraic spaces and their compactifications, the goal here is to construct a "horizontal completion" of an arithmetic quotient of a Mumford-Tate domains. Mumford-Tate domains are flag domains - they are open G(R)-orbits in generalized flag manifolds G(C)/P.
The minicourse consists of three talks:
1. Function theory on weakly symmetric spaces
2. Semisimple weakly symmetric spaces
3. Nilpotent weakly symmetric spaces