Arithmetic of inertia in braids groups and Grothendieck-Teichmüller theory – Benjamin Collas (Bayreuth Universität)

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Sala Riunioni (Dip. Matematica).

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 Mg,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 M0,4. 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.

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