BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Filip Rindler (University of Warwick) DTSTART:20261119T090000Z DTEND:20261119T110000Z DTSTAMP:20261028T031723Z UID:NCTS-GMT/40 DESCRIPTION:Title: Concentration Phenomena\, the Vanishing Mass Conjecture\, and an anisotr opic Michael-Simon inequality\nby Filip Rindler (University of Warwick ) as part of NCTS international Geometric Measure Theory seminar\n\n\nAbst ract\nConcentrating (that is\, $L^1$-bounded but not equi-integrable) sequ ences of functions satisfying a linear PDE constraint\, such as curl- or d ivergence-freeness\, arise in many situations within PDE theory\, the calc ulus of variations\, and geometric measure theory. I will present recent w ork proving that every Young measure generated by a concentrating sequence admits a Choquet-type decomposition into simpler concentration Young meas ures whose barycenters lie in the Tartar wave cone associated to the diffe rential constraint. This resolves Bouchitté’s 2001 Vanishing Mass Conje cture and also yields a number of applications\, including to compensated compactness\, the structure of the singular part of PDE-constrained measur es\, and Morrey’s Conjecture in the calculus of variations. The main new ingredients of the proof are "barrier functions" for convex cones and a s moothing argument based on the heat flow. I will also discuss a further ap plication to scale-invariant bounds for measures on "thin" sets\, which fu rthermore implies a general anisotropic Michael-Simon inequality for varif olds (the first version of this last application was found by AI based on the ideas in the proof of the Vanishing Mass Conjecture).\n\nThis is joint work with Luca Gennaioli (for the Vanishing Mass Conjecture) and Guido De Philippis\, Luca Gennaioli\, Alessandro Pigati (for the scale-invariant b ounds and the Michael-Simon inequality).\n\nPreprints: https://arxiv.org/a bs/2608.20899 and https://arxiv.org/abs/2609.34573\n LOCATION:https://researchseminars.org/talk/NCTS-GMT/40/ END:VEVENT END:VCALENDAR