Algebra/Topology seminar by Pedro Boavida de Brito

Algebra/Topology seminar by Pedro Boavida de Brito (Lisbon)

Title: Operads of genus zero curves and the Grothendieck-Teichmuller group

Abstract: In Esquisse d’un programme, Grothendieck made the fascinating suggestion that the absolute Galois group of the rationals could be understood via its action on a "Teichmuller tower", the collection of (profinite) mapping class groups of surfaces of all genera and the natural relations between them. In this talk, I plan to describe a genus zero analogue of this story from the point of view of operad theory. The result is that the group of homotopy automorphisms of the (profinite) genus zero Teichmuller tower agrees with the Grothendieck-Teichmuller group, an object which is closely related to the absolute Galois group of the rationals. This is joint work with Geoffroy Horel and Marcy Robertson.