Graduate Student / Postdoc Seminar

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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.