Sean McCurdy, University of Washington

PDL C401
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 handwaving, a few big ideas, some formal nonsense, and a parade of pictures of sets covered by balls. No prior knowledge is assumed.