EVENT DETAILS AND ABSTRACT

Title: Schrodinger solutions on sparse and spread-out sets
Speaker: Xiumin Du
Speaker Info: University of Maryland
Brief Description:
Special Note:
Abstract:

If we want the solution to the Schrodinger equation to converge to its initial data pointwise, what's the minimal regularity condition for the initial data should be? I will present recent progress on this classic question of Carleson. This pointwise convergence problem is closely related to other problems in PDE and geometric measure theory, including spherical average Fourier decay rates of fractal measures, Falconer's distance set conjecture, etc. All these problems essentially ask how to control Schrodinger solutions on sparse and spread-out sets, which can be partially answered by several recent results derived from induction on scales and Bourgain-Demeter's decoupling theorem.