positivity questions in K\"ahler-Einstein theory"

positivity questions in K\"ahler-Einstein theory"

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Luca Di Cerbo, Duke University
Fine Hall 314

In this talk, I describe how the existence of both complete and incomplete K"ahler-Einstein(KE) metrics on quasi-projective 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.