Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

John Voight
Affiliation:

Dartmouth College
Date:

Wed, 20/04/2022 - 14:30 - 15:30 Contact person for this talk and zoom details: Harry Smit (smit@mpim-bonn.mpg.de)

The study of the classical modular curves has rewarded

mathematicians for perhaps a century. Triangular modular curves are a

certain generalization of modular curves that arise from quotients of

the upper half-plane by congruence subgroups of hyperbolic triangle

groups. Despite being nonarithmetic in almost all cases, they

nevertheless carry several appealing features in common with the

classical case: for example, they are defined over explicitly given

number fields, and they have a moduli interpretation over the complex

numbers (by work of Cohen-Wolfart). We report on progress to extend

this moduli interpretation, exhibiting a canonical model for triangular

modular curves and their modular embeddings into quaternionic and

unitary Shimura varieties. This is joint work with Robert A. Kucharcyzk.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/246