Bruno Klingler

Symmetric differentials and fundamental group

Abstract: Given X a smooth complex projective variety, exterior differentials on X controls the Hodge theory of X, in particular its cohomology (and hopefully its motive). What about symmetric differentials ? In this talk I will discuss how they control the (topological) fundamental group of X, in particular its rigidity properties. As a main application and illustration,  I will explain striking new rigidity properties for ball quotients using automorphic forms.