A pleasant surprise of the cyclotomic character

In 1990, V. Drinfeld introduced the Grothendieck-Teichmueller group GT. This group receives a homomorphism from the absolute Galois group G_Q of rational numbers, and this homomorphism is injective due to Belyi's theorem. In his 1990 ICM talk, Y. Ihara posed a very hard question about the surjectivity of this homomorphism from G_Q to GT.

In my talk, I will introduce the groupoid of GT-shadows and show how this groupoid is related to the group GT. I will formulate a version of Ihara's question for GT-shadows and describe a family of objects of the groupoid for which this question has a positive answer. My talk is loosely based on the joint paper with I. Bortnovskyi, B. Holikov and V. Pashkovskyi.