Abstract: Consider the following problem, originally posed by Gizatullin: « Which automorphisms of a smooth quartic K3 surface in are induced by Cremona transformations of the ambient space? » When S  is a smooth quartic surface in , the pair (,S) is an example of a Calabi-Yau pair, that is, a mildly singular pair (X,D) consisting of a normal projective variety X and an effective Weil divisor D on X such that . In this talk, I will explain a general framework to investigate the birational geometry of Calabi-Yau pairs and how this can be applied to approach Gizatullin’s problem. This is a joint work with Alessio Corti and Alex Massarenti.