A classical theorem in Riemannian geometry asserts that products of compact manifolds cannot admit Riemannian metrics with negative sectional curvature. A fibration (or a fibre bundle) is a natural generalization of a product and hence one can ask if a fibration can admit such a metric. This question is still open and I will discuss it in the context of Kahler manifolds. This leads to the study of graphs of holomorphic motions, which originally arose in complex dynamics. I will sketch a proof that the graph cannot be biholomorphic to a ball or more generally, a strongly pseudoconvex domain.

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- Seminars for 2016