BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Filip Rindler (University of Warwick) DTSTART:20230118T130000Z DTEND:20230118T150000Z DTSTAMP:20260423T041343Z UID:NCTS-GMT/14 DESCRIPTION:Title: Singularities\, Rectifiability\, and PDE-constraints\nby Filip Rindl er (University of Warwick) as part of NCTS international Geometric Measure Theory seminar\n\n\nAbstract\nSurprisingly many different problems of Ana lysis naturally lead to questions about singularities in (vector) measures . These problems come from both "pure" Analysis\, such as the question for which measures Rademacher's theorem on the differentiability of Lipschitz functions holds\, and its non-Euclidean analogues\, as well as from "appl ied" Analysis\, for example the problem to determine the fine structure of slip lines in elasto-plasticity. It is a remarkable fact that many of the (vector) measures that naturally occur in these questions satisfy an (und er-determined) PDE constraint\, e.g.\, divergence- or curl-freeness. The c rucial task is then to analyse the fine properties of these \nPDE-constrai ned measures\, in particular to determine the possible singularities that may occur. It turns out that the PDE constraint imposes strong restriction s on the shape of these singularities\, for instance that they can only oc cur on a set of bounded Hausdorff-dimension\, or even that the measure is k-rectifiable where its upper k-density is positive. The essential difficu lty in the analysis of PDE-constrained measures is that many standard meth ods from harmonic analysis are much weaker in an L$^1$-context and thus ne w strategies are needed. In this talk\, I will survey recent and ongoing w ork on this area of research.\n LOCATION:https://researchseminars.org/talk/NCTS-GMT/14/ END:VEVENT END:VCALENDAR