Title: A pleasant surprise of the cyclotomic character
Abstract: 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 https://arxiv.org/abs/2405.11725 with
I. Bortnovskyi, B. Holikov and V. Pashkovskyi.