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A part of Grothendieck's program for studying the Galois group $G_{\mathbbQ}$ of the field of all algebraic numbers $\overline{\mathbb Q}$ emerged fromhis insight that one should lift its action upon $\overline{\mathbb Q}$ to theaction of $G_{\mathbb Q}$ upon the (appropriately defined) profinite completionof $\pi_1({\mathbb P}^1 \setminus \{0,1, \infty\})$. The latter admits a goodcombinatorial encoding via finite graphs "dessins d'enfant". This part wasactively developing during the last decades, starting with foundational worksof A. Belyi, V. Drinfeld and Y. Ihara. Our brief note concerns another part ofGrothendieck program, in which its geometric environment is extended to modulispaces of algebraic curves, more specifically, stable curves of genus zero withmarked/labelled points. Our main goal is to show that dual graphs of suchcurves may play the role of "modular dessins" in an appropriate operadiccontext.

Dessins for Modular Operad and Grothendieck-Teichmuller Group