BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Max Engelstein (University of Minnesota) DTSTART:20200618T140000Z DTEND:20200618T145000Z DTSTAMP:20260423T035610Z UID:IMS/28 DESCRIPTION:Title: An Epiperimetric Approach to Isolated Singularities\nby Max Engelstein (U niversity of Minnesota) as part of PDE seminar via Zoom\n\n\nAbstract\nThe presence of singular points (i.e. points around which the object in quest ion does not look flat at any scale) is inevitable in most minimization pr oblems. One fundamental question is whether minimizers have a unique tange nt object at singular points i.e.\, is the minimizer increasingly well app roximated by some other minimizing object as we “zoom in” at a singula r point. This question has been investigated with varying degrees of succe ss in the settings of minimal surfaces\, harmonic maps and obstacle proble ms amongst others.\n\nIn this talk\, we will present an uniqueness of blow ups result for minimizers of the Alt-Caffarelli functional. In particular\ , we prove that the tangent object is unique at isolated singular points i n the free boundary. Our main tool is a new approach to proving (log-)epip erimetric inequalities at isolated singularities. This epiperimetric inequ ality differs from previous ones in that it holds without any additional a ssumptions on the symmetries of the tangent object.\n\nIf we have time\, w e will also discuss how this method allows us to recover some uniqueness o f blow-ups results in the minimal surfaces setting\, particularly those of Allard-Almgren (’81) and Leon Simon (’83). This is joint work with Lu ca Spolaor (UCSD) and Bozhidar Velichkov (U. Napoli).\n\nhttps://nguyenquo chung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n LOCATION:https://researchseminars.org/talk/IMS/28/ END:VEVENT END:VCALENDAR