This talk will be on the space of stability conditions for the total space of the cotangent bundle on P^2. Its geometry is related to classical questions on Chern classes of stable vector bundles P^2, to the modular group Gamma_1(3), and, via mirror symmetry, to the moduli space of elliptic curves with Gamma_1(3)-level structure. This is based on joint work with Emanuele Macrì.