positivity questions in K\"ahlerEinstein theory"
positivity questions in K\"ahlerEinstein theory"

Luca Di Cerbo, Duke University
Fine Hall 314
In this talk, I describe how the existence of both complete and incomplete K"ahlerEinstein(KE) metrics on quasiprojective varieties motivates a number of questions around the theme of positivity in complex geometry. After describing in some details the case of complex surfaces, I discuss some higher dimensional results. Finally, I describe some applications not directly connected with the theory of singular KE metrics. For example, I show how to count the number of maximal parabolic subgroups in neat arithmetic lattices of the Bergman ball.