See
MR2264540 (2007j:14028) Lochak, Pierre(F-PARIS6-IMJ); Schneps, Leila(F-PARIS6-IMJ) Open problems in Grothendieck-Teichmüller theory. Problems on mapping class groups and related topics, 165–186, Proc. Sympos. Pure Math., 74, Amer. Math. Soc., Providence, RI, 2006. 14G32 (18F30 20F34 57M07)
And anything else by Leila Schneps.
