EVENT DETAILS AND ABSTRACT

Title: Fourier extension operator on sparse domain
Speaker: Xiumin Du
Speaker Info: NU
Brief Description:
Special Note:
Abstract:

If a function has Fourier support on the (truncated) paraboloid, then what can we tell about its behavior on a set of a lower dimension in physical space? This question relates to several problems in PDEs and geometric measure theory. In this talk, I'll introduce several results derived from decoupling and induction on scales, which allows us to control the Fourier extension operator (or Schroedinger solutions) on a sparse and spread-out set. This talk is based on my joint work with Larry Guth, Xiaochun Li, and Ruixiang Zhang.