Appears in collection : 2018 - T1 - WS3 - Model theory and applications

From the work of Freitag and Scanlon, we have that the ODEs satisfied by the Hauptmoduls of arithmetic subgroups of SL2(Z) are strongly minimal and geometrically trivial. A challenge is to now show that same is true of ODEs satisfied by the Hauptmoduls of all (remaining) Fuchsian triangle groups. The aim of this talk is to both explain why this an interesting/important problem and also to discuss some of the progress made so far.