Endpoint convergence for the planar Schrodinger equation

We resolve the planar Sobolev endpoint of Carleson's convergence problem: for initial data in $H^{1/3}({\mathbb{R}}^2)$, the Schrödinger evolution converges almost everywhere to the initial data as $t\downarrow 0$. The evolution is defined by taking the Gaussian regularization limit first; on one full-measure spatial set, this limit exists for every $0<t<1$, and the resulting evolution is continuous at t = 0.