There's a literature about dessins d'enfants (including [my previous question here][1]), and one amazing thing about them is that absolute Galois group `Gal Q` acts on cartographic group which, I believe, is isomorphic to  `letters_2 = <<A, B>>` (group, freely generated by two noncommuting letters).


The funny thing about the latter group is that there is a flat connection coming from string theory defined on its group algebra, `C[letters_2]`, which I think has the name of Knizhnik-Zamolodchikov. So, it that latter connection somehow related to Galois group?


  [1]: http://mathoverflow.net/questions/1909/what-are-dessins-denfants