Computational Algebra Seminar

Let H be the upper half complex plane. The classical modular curves X_0(N) are defined as quotients of H by finite index subgroups of PSL_2(Z). The class X_0^D(N) of Shimura curves are defined analogously, generalising X_0(N), in terms of the actions on H of twisted matrix groups coming from subgroups of units in indefinite quaternion rings. I will define the relevant class of groups and their actions on the upper half plane, and describe the computational problem of determining a fundamental domain, illustrated with examples.