ABSTRACT: Suppose $X$ is a complex algebraic curve (Riemann surface) embedded in its Jacobian variety $J$.  If $X$ has genus at least two, the Manin-Mumford conjecture (proved by Raynaud) asserts that the intersection
of $X$ with the torsion subgroup $T$ of $J$ is finite.  Explicitly determining this intersection for a specific curve $X$ can be very difficult.  Coleman, Kaskel, and Ribet conjectured that when $X$ is the modular curve $X_0(p)$, embedded in its Jacobian $J_0(p)$ via one of the two cusps, the intersection of $X$ and $T$ consists of just the cusps for almost all prime numbers $p$.  We will sketch a proof of this conjecture which exploits the interplay between the geometry of $X_0(p)$ and the action of the Galois group of ${\mathbb Q}$ on torsion points on $J_0(p)$.