I will talk about Bruno Klingler's paper in which he explores the link between representations of the fundamental group and vanishing of global symmetric differentials on quotients of bounded symmetric domains. For each irreducible classical bounded symmetric domain D, he computes smallest symmetric power of the cotangent bundle of a smooth projective quotient X of D that admits a global section. The proof of this result is geometric and uses some deep vanishing results due to Mok. If time permits, I will talk about how to extend Klingler's results to the klt setting.
