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Inflection points of real and tropical plane curves

We construct maximal real algebraic curves of any degree d at least 3 in the projective plane with the maximal number of real inflection points, answering to a question posed by Arnol'd. To construct these curves, we follow a tropical approach. Namely, we study tropical limits of inflection points of classical plane algebraic curves. The main tropical tool we use to understand these tropical inflection points are tropical modifications.