Student Harmonic Analysis and PDE Seminar (HADES): A Sharp Schrödinger Maximal Estimate in $\mathbb R^2$
Seminar | September 12 | 3:40-5 p.m. | 891 Evans Hall
Kevin O'Neill, UC Berkeley
In this talk, I will present a recent paper of Xiumin Du, Larry Guth, and Xiaochun Li, which proves almost everywhere convergence of solutions to the Schrödinger equation in $\mathbb R^2$ for initial data in $H^s (s >1/3)$. I will give an extended introduction to the method of polynomial partitioning, which is used in the proof of their main theorem. A new result which arises during the proof is a bilinear local refinement of the Strichartz inequality which is made possible by the $l^2$-decoupling theorem of Bourgain and Demeter.