# Graduate Student / Postdoc Seminar

#### Fine structure of measures satisfying a PDE constraint

**Speaker:**
Guido De Philippis, CIMS

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, December 6, 2019, 1 p.m.

**Synopsis:**

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 later work joint 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, of their applications and I will present some new open problems and new lines of research.