Green Function vs. Geometry

Explore the relationship between Green functions and geometry in this 48-minute lecture by Svitlana Mayboroda from the Hausdorff Center for Mathematics. Delve into the main result establishing that d-dimensional sets in R^n are regular (uniformly rectifiable) if and only if the Green function for elliptic operators is well approximated by affine functions (distance to the hyperplanes) in all dimensions d less than n. Gain insights into the intersection of mathematical analysis and geometry through this advanced exploration of Green functions and their geometric implications.