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Here we go, again: the Almgren frequency function, or, yet another inductively-refined covering argument

Sean McCurdy, University of Washington
Thursday, April 27, 2017 - 2:30pm to 3:30pm
PDL C-401

Abstract:  This talk is aimed at introducing the Almgren frequency function and using it as an example to illustrate the power of monotonicity formulae in Geometric Measure theory.  Specifically, we will outline the way in which Cheeger, Naber and Valtorta employed it to get new (as of 2013) results on the Minkowski dimension of the critical set of harmonic functions and solutions to elliptic PDEs with Lipschitz coefficients.  There will be lots of hand-waving, a few big ideas, some formal nonsense, and a parade of pictures of sets covered by balls.  No prior knowledge is assumed.

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