August 28, 2022 to September 2, 2022
Europe/Zurich timezone

Automorphisms of seemed surfaces, modular operads and Galois actions

Sep 1, 2022, 11:10 AM


Marcy Robertson (Melbourne)


The idea behind Grothendieck-Teichmüller theory is to study the absolute Galois group via its actions on (the collection of all) moduli spaces of genus 𝑔 curves. In practice, this is often done by studying an intermediate object: The Grothendieck-Teichmüller group, GT. In this talk, I’ll describe an algebraic gadget built from simple decomposition data of Riemann surfaces. This gadget, called an infinity modular operad, provides a model for the collection of all moduli spaces of genus 𝑔 curves with 𝑛 boundaries, which we justify by showing that the automorphisms of this algebraic object is isomorphic to a subgroup of Grothendieck-Teichmüller group. This is joint work with L. Bonatto.

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