Appears in collection : Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)

In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of the unipotent completion of the fundamental group of the projective line with 3 points. It is now known to be motivic by Deligne-Goncharov and generates the category of mixed Tate motives over the integers. It is closely related to many classical objects such as polylogarithms and multiple zeta values, and has a wide range of applications from number theory to physics.