“An Elementary Approach to Dessins d’enfants and the Grothendieck-Teichmüller Group” by Pierre Guillot

Pierre Guillot has a new paper on the ArXiv entitled “An Elementary Approach to Dessins d’enfants and the Grothendieck-Teichmüller Group”.

Abstract. We give an account of the theory of dessins d’enfants which is both elementary and self-contained. We describe the equivalence of many categories (graphs embedded nicely on surfaces, finite sets with certain permutations, certain field extensions, and some classes of algebraic curves), some of which are naturally endowed with an action of the absolute Galois group of the rational field. We prove that the action is faithful. Eventually we prove that this absolute Galois group embeds into the Grothendieck-Teichmüller group GT_0 introduced by Drinfel’d. There are explicit approximations of GT_0 by finite groups, and we hope to encourage computations in this area.
Our treatment includes a result which has not appeared in the literature yet: the Galois action on the subset of regular dessins – that is, those exhibiting maximal symmetry — is also faithful.

You can download the paper here. Thanks to Lily Khadjavi for letting me know about this wonderful reference!


About Edray Herber Goins, Ph.D.

Edray Herber Goins grew up in South Los Angeles, California. A product of the Los Angeles Unified (LAUSD) public school system, Dr. Goins attended the California Institute of Technology, where he majored in mathematics and physics, and earned his doctorate in mathematics from Stanford University. Dr. Goins is currently an Associate Professor of Mathematics at Purdue University in West Lafayette, Indiana. He works in the field of number theory, as it pertains to the intersection of representation theory and algebraic geometry.
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