The action of Grothendieck-Teichmueller (GT) shadows on child's drawings

Abstract: Grothendieck-Teichmueller (GT) shadows can be thought of as approximations of elements of the mysterious Grothendieck-Teichmueller group GT introduced by V. Drinfeld in 1990. GT-shadows are morphisms of a groupoid GTSh whose objects are certain finite index normal subgroups of the Artin braid group. The groupoid GTSh is closely connected to group GT and to the absolute Galois group $G_Q$ of rational numbers. GTSh acts on Grothendieck's child's drawings and this action is compatible with those of the groups $G_Q$ and GT. In my talk, I will present the hierarchy of orbits of child's drawings with respect to the actions of $G_Q$, GT and GTSh, give selected examples and say a few words about future directions of this research. This talk is loosely based on my paper "The Action of GT-Shadows on Child's Drawings" (J. of Algebra, 2025). In many respects, the exploration of the action of GT-Shadows on child's drawings is inspired by a paper written by D. Harbater and L. Schneps in 1997.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper )

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MIT number theory seminar

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