UCLA

This thesis studies scaling critical Strichartz estimates for the Schrödinger flow on compact symmetric spaces. A general scaling critical Strichartz estimate (with an ε-loss, respectively) is given conditional on a conjectured dispersive estimate (with an ε-loss, respectively) on general compact symmetric spaces. The dispersive estimate is then proved for the special case of connected compact Lie groups. Slightly more generally, for products of connected compact Lie groups and spheres of odd dimension, the dispersive estimate is proved with an ε-loss.