This talk will focus on special loci in the moduli of curves, parametrizing curves that have special automorphisms groups. These loci give information about the Grothendieck-Teichmuller group GT of Drinfeld, which has been shown to contain the absolute Galois group of the rational numbers. It is unknown whether these two groups are equal, or how far apart they are. This geometric approach via special loci in moduli gives new insights into GT and indirectly into the absolute Galois group of Q.