Quantifier elimination in algebraically closed valued fields in the analytic language: a geometric approach

I will present a work on flattening by blow-ups in the context of Berkovich geometry (inspired by Raynaud and Gruson’s paper on the same topic in the scheme-theoretic setting), and explain how it gives rise to the description of the image of an arbitrary analytic map between two compact Berkovich spaces, and why this description is (very likely) related to quantifier elimination in the Lipshitz-Cluckers variant of Lipshitz-Robinson’s analytic language. (I plan to spend most of the talk discussing the results rather than their proofs.)