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Tuesday, October 10, 2017

**Abstract:** Recently, Guth, Du and I solved the pointwise convergence problem of Schrodinger equations in two-dimensional case. We prove that the solution to free Schrodinger equation in R^2 converges to its initial data, provided the initial data belongs to H^s for s larger than 1/3. This result is sharp, up to the end point, due to Bourgain's example. The proof relies on the polynomial partitioning method and the decoupling method.