Hypergeometric Galois Actions

TL;DR

This paper proposes studying the Galois action on hypergeometric dessins, which are special modular graphs linked to Thurston's sphere triangulations, aiming for explicit calculations due to their connection with hypergeometric functions.

Contribution

It introduces a project to analyze Galois actions on a specific class of modular graphs arising from Thurston's sphere triangulations, leveraging their hypergeometric function connections.

Findings

Potential for explicit Galois action calculations on these graphs

Connection established between hypergeometric functions and modular graphs

Framework for future algebraic and geometric investigations

Abstract

We outline a project to study the Galois action on a class of modular graphs (special type of dessins) which arise as the dual graphs of the sphere triangulations of non-negative curvature, classified by Thurston. Because of their connections to hypergeometric functions, there is a hope that these graphs will render themselves to explicit calculation for a study of Galois action on them, unlike the case of a general dessin.