There was an observation that any algebraic curve over Q can be rationally mapped to P^1 without three points and this led Grothendieck to define a special class of these mappings, called the Children's Drawings, or, in French, Dessins d'Enfantesd'Enfants (his quote was something like "things as simple as the drawings...").

I'm not an expert in this field, so could somebody please write more about those dessins, and what things they are related to? What's their importance? How does the cartographic group act on these?

There was an observation that any algebraic curve over Q can be rationally mapped to P^1 without three points and this led Grothendieck to define a special class of these mappings, called the Children's Drawings, or, in French, Dessins d'Enfantes (his quote was something like "things as simple as the drawings...").

I'm not an expert in this field, so could somebody please write more about those dessins, and what things they are related to? What's their importance? How does the cartographic group act on these?