Local smoothing for the wave equation

Larry Guth, Massachusetts Institute of Technology

*Note the time change*

Zoom link:  https://princeton.zoom.us/j/99136657600

Passcode required

(The colloquium password will be distributed to Princeton University and IAS members. We ask that you do not share this password. If you would like to be included in the colloquium and are not a member of either institution, please email the organizer Casey Kelleher (caseyk@princeton.edu) with an email requesting to participate which introduces yourself, your current affiliation and stage in your career.)

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 the colloquium, 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.