the 2-spin spherical sherrington kirkpatrick (ssk) model was introduced by kosterlitz, thouless and jones as a simplification of the usual sherrington-kirkpatrick model with ising spins. the ssk model admits tractable formulas for many of its observables, allowing for a detailed analysis of its fluctuations using techniques from random matrix theory. we discuss recent results on the fluctuations of the ssk model with a magnetic field as well as at critical temperature. based on joint work with p. sosoe.