  We study the Schr\"odinger equation on a flat euclidean cone $\mathbb{R}_+
\times \mathbb{S}^1_\rho$ of cross-sectional radius $\rho > 0$, developing
asymptotics for the fundamental solution both in the regime near the cone point
and at radial infinity. These asymptotic expansions remain uniform while
approaching the intersection of the "geometric front", the part of the solution
coming from formal application of the method of images, and the "diffractive
front" emerging from the cone tip. As an application, we prove Strichartz
estimates for the Schr\"odinger propagator on this class of cones.
