REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: In 1990, V. Drinfeld introduced the Grothendieck-Teichmueller group GT. This group receives the 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 show that there are situations when the version of Ihara's question for GT-shadows has a positive answer. My talk is based on a joint work with I. Bortnovskyi, B. Holikov and V. Pashkovskyi.