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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.

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