# Arithmetic of inertia in braids groups and Grothendieck-Teichmüller theory

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Benjamin Collas

created by daniele on 13 Apr 2015

16 apr 2015
-- 16:00

Aula Riunioni, DM, Pisa

Seminari di Algebra, Topologia e Combinatoria, Pisa

**Abstract.**

Following Grothendieck's "Esquisse d'un programme", Grothendieck-Teichmüller theory is the study of the absolute Galois group of rational through combinatorial properties of the moduli spaces of curves $M_{g,n}$. Originally developed by Drinfel'd and Ihara in the context of quantum groups and arithmetic geometry, it is guided by the existence a certain stratification of the space which then translates in term of inertia when considered from the fundamental group point of view.

We will present the main ideas of a Grothendieck-Teichmüller theory by considering first the case of curves of genus zero and its relation with the Artin braid groups -- all the needed notions will be given in detail within the case of M_{{0,4}.} By then considering the Artin braid groups as a special case of generalized braid groups, we will explain how these ideas can be adapted, and may lead to a similar ``Grothendieck-Dynkin'' theory, when studying the geometry of the wonderful model compactification of hyperplane arrangements.

Il seminario sarà diviso in due parti di 45' ciascuna.
La prima parte del seminario sarà introduttiva e comprensibile a studenti di dottorato o laurea specialistica in matematica.