Talk Abstract: In this talk I will present some new result concerning the structure of measure satisfying a linear PDE constraint. In 2016, in collaboration with Filip Rindler, we prove a first structural result concerning the singular part of measure subject to PDE constraint. This turned out to have several applications in GMT and in Geometric Analysis.

In a joint work with Adolfo Arroyo Rabasa, Jonas Hirsch and Filip Rindler we improve upon this result proving a more precise structure on the "low" dimensional part of the measure. As a corollary we recover several known rectifiability results. In this talk I will try to give an overview of both these results and of their applications.

Bio: Guido De Philippis is an Italian mathematician. He earned his PhD at Scuola Normale Superiore in 2012 under the supervision of Luigi Ambrosio and Luis Caffarelli. He is currently a professor at NYU.

His research interests mostly lie in the area of GMT, Calculus of Variation and PDE: