19 nov 2026 — 10:00   [open in google calendar]

Agenda: Get-together (30 min), presentation Filip Rindler (60 min), questions and discussions (30 min).

Abstract.

Concentrating (that is, $L^1$ -bounded but not equi-integrable) sequences of functions satisfying a linear PDE constraint, such as curl- or divergence-freeness, arise in many situations within PDE theory, the calculus of variations, and geometric measure theory. I will present recent work proving that every Young measure generated by a concentrating sequence admits a Choquet-type decomposition into simpler concentration Young measures whose barycenters lie in the Tartar wave cone associated to the differential constraint. This resolves Bouchitté’s 2001 Vanishing Mass Conjecture and also yields a number of applications, including to compensated compactness, the structure of the singular part of PDE-constrained measures, and Morrey’s Conjecture in the calculus of variations. The main new ingredients of the proof are "barrier functions" for convex cones and a smoothing argument based on the heat flow. I will also discuss a further application to scale-invariant bounds for measures on "thin" sets, which furthermore implies a general anisotropic Michael-Simon inequality for varifolds (the first version of this last application was found by AI based on the ideas in the proof of the Vanishing Mass Conjecture).

This is joint work with Luca Gennaioli (for the Vanishing Mass Conjecture) and Guido De Philippis, Luca Gennaioli, Alessandro Pigati (for the scale-invariant bounds and the Michael-Simon inequality).

Preprints: https://arxiv.org/abs/2608.20899 and https://arxiv.org/abs/2609.34573

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