BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Casey Rodriguez (MIT) DTSTART:20200807T203000Z DTEND:20200807T213000Z DTSTAMP:20260423T021649Z UID:MPHA/9 DESCRIPTION:Title: The Radiative Uniqueness Conjecture for Bubbling Wave Maps\nby Casey Rodr iguez (MIT) as part of TAMU: Mathematical Physics and Harmonic Analysis Se minar\n\n\nAbstract\nWe will discuss the finite time breakdown of solution s to a canonical example of a geometric wave equation: energy critical wav e maps. Breakthrough works of Krieger-Schlag–Tataru\, Rodnianski-Sterben z and Raphael–Rodnianski produced examples of wave maps that develop sin gularities in finite time. These solutions break down by concentrating ene rgy at a point in space (via bubbling a harmonic map) but have a regular l imit\, away from the singular point\, as time approaches the final time of existence. The regular limit is referred to as the radiation. This mechan ism of breakdown occurs in many other PDE including energy critical wave e quations\, Schrodinger maps and Yang-Mills equations. A basic question is the following:\n\nCan we give a precise description of all bubbling singul arities for wave maps with the goal of finding the natural unique continua tion of such solutions past the singularity?\n\nIn this talk\, we will dis cuss recent work (joint with J. Jendrej and A. Lawrie) which is the first to directly and explicitly connect the radiative component to the bubbling dynamics by constructing and classifying bubbling solutions with a simple form of prescribed radiation. Our results serve as an important first ste p in formulating and proving the following Radiative Uniqueness Conjecture for a large class of wave maps: every bubbling solution is uniquely chara cterized by its radiation\, and thus\, every bubbling solution can be uniq uely continued past blow-up time while conserving energy.\n LOCATION:https://researchseminars.org/talk/MPHA/9/ END:VEVENT END:VCALENDAR