BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Max Engelstein DTSTART:20200825T170000Z DTEND:20200825T180000Z DTSTAMP:20260423T021014Z UID:OSGA/25 DESCRIPTION:Title: Wi nding for Wave Maps\nby Max Engelstein as part of Online Seminar "Geom etric Analysis"\n\n\nAbstract\nWave maps are harmonic maps from a Lorentzi an domain to a\nRiemannian target. Like solutions to many energy critical PDE\, wave maps can\ndevelop singularities where the energy concentrates o n arbitrary small\nscales but the norm stays bounded. Zooming in on these singularities yields\na harmonic map (called a soliton or bubble) in the w eak limit. One\nfundamental question is whether this weak limit is unique\ , that is to say\,\nwhether different bubbles may appear as the limit of d ifferent sequences of\nrescalings.\n\nWe show by example that uniqueness m ay not hold if the target manifold is\nnot analytic.  Our construction is heavily inspired by Peter Topping's\nanalogous example of a ``winding" bu bble in harmonic map heat flow. However\,\nthe Hamiltonian nature of the w ave maps will occasionally necessitate\ndifferent arguments.  This is joi nt work with Dana Mendelson (U Chicago).\n LOCATION:https://researchseminars.org/talk/OSGA/25/ END:VEVENT END:VCALENDAR