Exploration of Grothendieck-Teichmueller (GT) shadows

Abstract: In 1990, V. Drinfeld introduced the Grothendieck-Teichmueller group GT. This mysterious group receives a homomorphism from the absolute Galois group $G_Q$ of rational numbers, and this homomorphism is injective due to Belyi's theorem. Grothendieck-Teichmueller (GT) shadows may be thought of as approximations of elements of the group GT. They are morphisms of a groupoid whose objects are certain finite index normal subgroups of the Artin braid group. Exploration of the groupoid of GT-shadows is motivated by very hard open problems that include Y. Ihara's question about the surjectivity of the homomorphism from $G_Q$ to GT. In my talk, I will introduce the groupoid of GT-shadows and describe its relation to the group GT. I will also present promising results and formulate selected open problems. My talk is loosely based on joint papers with I. Bortnovskyi, J.J. Guynee, B. Holikov and V. Pashkovskyi.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar