Alexandre Eimer

On a compact orientable connected Riemann surface, draw a few black dots, a few white ones, connect black ones to white ones, then you will get a children's drawing ; although it could at first seem childish, it opens some new perspectives : "an unexplored world" said Grothendieck himself. In this talk, we shall try to show the links between bigraphs on Riemann surfaces, covering spaces of the wedge of two circles, arithmetic algebraic curves and constellations : indeed the point of this theory is the profound and unexpected links between such different objects. We shall end by mentioning one of the reason which could lead to study the dessins d'enfants : the action of the absolute Galois group of Q on them.