Endpoint pointwise convergence for the Schrodinger equation in higher dimensions

We resolve the Sobolev endpoint of Carleson's pointwise convergence problem in every dimension n ≥ 3. For initial data in $H^{n/(2(n+1))}({\mathbb{R}}^n)$, the free Schrödinger evolution converges almost everywhere to the initial data as $t\downarrow 0$. The evolution is defined by removing Gaussian regularization on one full-measure spatial set, uniformly over the interval $0<t<1$.