The Pointwise Convergence Problem for the Free Schrödinger Equation (II)
Time: 2019-06-26
Published By: He Liu
Speaker(s): Ruixiang Zhang (University of Wisconsin-Madison)
Time: 14:00-15:30 June 27, 2019
Venue: Room 29, Quan Zhai, BICMR
Carleson proposed a problem on a.e. convergence for free Schrödinger solutions as time goes to zero. Recently it got a sharp answer (up to the endpoint) in all dimensions. In these two lectures we will talk about recent new results in dimensions n + 1 for n = 2 (Du-Guth-Li) and all n > 2 (by a joint work of Xiumin Du and myself). We will also talk about some crucial ideas/tools behind them (polynomial partitioning, the Bourgain-Guth induction, decoupling, refined Strichartz and multilinear refined Strichartz, a "fractal" L^2 estimate) and relevant problems.
