U. Haifa Topology & Geometry seminar: Wednesday, March 18, 2026, 13:00. Speaker: Vasily Dolgushev (Temple University). Title: “Grothendieck-Teichmuller shadows and their action on child’s drawings”.
In 1990, V. Drinfeld introduced the Grothendieck-Teichm¨uller group GT. This group receives the homomorphism from the absolute Galois group GQ of rational numbers and this homomorphism is injective due to Belyi’s theorem. Many challenging questions about GT are motivated by its link to GQ and to its action on Grothendieck’s child’s drawings. Some of these questions can be investigated by GT-shadows. These gadgets are morphisms of a groupoid assembled from the Artin braid group on three strands, and one can think of GT-shadows as approximations of elements of GT. In my talk, I will recall the groupoid of Grothendieck-Teichm¨uller GT shadows and its action on child’s drawings.I will show how GT-shadows can be used to construct finite non-abelian quotients of GT and prove that the natural homomorphisms from GQ to these quotients are surjective. If time permits, I will mention open questions related to GT-shadows and their action on child’s drawings.My talk is partially based on joint paper https://arxiv.org/abs/2405.11725 with I. Bortnovskyi, B. Holikov, and V. Pashkovskyi.
