Benoît Bertrand, Institut de mathématiques de Toulouse
A smooth cubic is a genus one planar curve. A tropical cubic in contrast can be smooth, planar or not and of any genus. The trick is that in the tropical case the maximal genus of a curve also depends of the dimension of the space in which it is embedded. I’ll try to show some pictures to convince you of these facts and explain our construction which we prove to be optimal for a fixed codimension. Despite the title, the talk will be in (my broken) English.
Joint with Erwan Brugallé and Lucía López de Medrano.