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Title: The infinite dimensional hyperbolic space of the Cremona group

Abstract:

In recent years one of the main tool in the study of the Cremona group is an action on an infinite dimensional hyperbolic space. In particular this was the key to get a Tits alternative for this group, and also for a proof of the non simplicity. My aim in this talk will be to give a gentle introduction to this construction, which relies on the notion of blowing-up a point in an algebraic surface (infinitely many times!).