Triangular modular curves

Triangular modular curves are a generalization of modular curves and arise as quotients of the complex upper half-plane by congruence subgroups of hyperbolic triangle groups. These curves naturally parameterize hypergeometric abelian varieties, making them interesting arithmetic objects. In this talk, we will focus on the Borel-kind triangular modular curves. We will show that when restricting to prime level, there are finitely many such curves of any given genus, and there is an algorithm to enumerate them. Time permitting, we will explore generalizations to composite level. This is joint work with John Voight.