COW SEMINAR: Ball quotients and moduli spaces

A number of moduli problems are, via Hodge theory, closely related to 
ball quotients. In this situation there is often a choice of possible 
compactifications such as the GIT compactification´and its Kirwan 
blow-up or the Baily-Borel compactification and the toroidal 
compactificatikon. The relationship between these compactifications is 
subtle and often geometrically interesting. In this talk I will discuss 
several cases, including cubic surfaces and threefolds and 
Deligne-Mostow varieties. This discussion links several areas such as 
birational geometry, moduli spaces of pointed curves, modular forms and 
derived geometry. This talk is based on joint work with S. 
Casalaina-Martin, S. Grushevsky, S. Kondo, R. Laza and Y. Maeda.