The APDE seminar on Monday, 3/29, will be given by Larry Guth online via Zoom from 4:10 to 5:00pm. To participate, email Georgios Moschidis (firstname.lastname@example.org) or Federico Pasqualotto (email@example.com).
Title: Local smoothing for the wave equation.
Abstract: The local smoothing problem asks about how much solutions to the wave equation can focus. It was formulated by Chris Sogge in the early 90s. Hong Wang, Ruixiang Zhang, and I recently proved the conjecture in two dimensions.
In this talk, we will build up some intuition about waves to motivate the conjecture, and then discuss some of the obstacles and some ideas from the proof.