After recalling the relevant definitions, I will explain how one can view the Grothendieck-Teichmüller group as the group of automorphisms of the operad of moduli spaces of genus zero Riemann surfaces. If time permits, I will also explain a homotopical version of this result which is due to Pedro Boavida de Brito, Marcy Robertson and myself.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/8767