Vasily Dolgushev, Temple University

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.