BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Spyros Alexakis (University of Toronto) DTSTART:20240201T143000Z DTEND:20240201T153000Z DTSTAMP:20260423T023042Z UID:jomarec/31 DESCRIPTION:Title: Squeezing a fixed amount of gravitational energy to arbitrarily small sca les\, in U(1) symmetry\nby Spyros Alexakis (University of Toronto) as part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbs tract\nWe discuss a construction of polarized U(1) space-times of a “fix ed size”\, where the initial data contains a given amount η>0 of incomi ng gravitational energy which is allowed to be supported at arbitrarily sm all scales\, without affecting the time of existence. More specialized exa mples can be constructed where any chosen fraction of this initial incomin g energy can stay focused along a null geodesic\, in the U(1) picture. We discuss the relationship of this result with one direction of Thorne’s h oop conjecture. The work relies on a special structure of the Einstein equ ations in this symmetry class\, a new re-scaling of the equations and larg e-time control\, along with a new local Klainerman-Sobolev estimate. Time permitting\, some comparisons of the result and the methods with large-dat a constructions for the Einstein equations over the last decade will also be presented.\n LOCATION:https://researchseminars.org/talk/jomarec/31/ END:VEVENT END:VCALENDAR