Triangular modular curves

Triangular modular curves are a generalization of modular curves and arise from quotients of the complex upper half-plane by congruence subgroups of hyperbolic triangle groups. They are connected to Darmon’s program for rational points on generalized Fermat equations.  In this talk, we will focus on arithmetic properties of the Borel-kind triangular modular curves and potential applications to Darmon’s program. This is joint work with John Voight.