Local smoothing for the wave equation
Local smoothing for the wave equation
*Note the time change*
Zoom link:ÌýÌý
±Ê²¹²õ²õ³¦´Ç»å±ðÌý°ù±ð±ç³Ü¾±°ù±ð»å
(The colloquium passwordÌýwill be distributed to Princeton University and IAS members. We ask that youÌýdo not share this password. If you would like to be included in the colloquiumÌýand 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.Ìý It was formulated by Chris Sogge in the early 90s.Ìý 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.