The Pointwise Convergence Problem for the Free Schrödinger Equation (I)
发布时间：2019年06月26日
浏览次数：5619
发布者: He Liu
主讲人： Ruixiang Zhang (University of Wisconsin-Madison)
活动时间： 从 2019-06-25 14:00 到 15:30
场地： 北京国际数学研究中心，全斋全29教室
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.
