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A Gentle Introduction to Uniform Rectifiability

Emily Casey, University of Washington
Thursday, February 9, 2023 - 12:30pm to 1:30pm
PDL C-401

A set is rectifiable if it is almost the image of countably many nice maps. So, what should it mean for a set to be uniformly rectifiable? How can we quantify this qualitative notion, that is, how can we record how much of our set is covered by a nice map at each scale? In the 1991 monograph, Singular Integrals and Rectifiable Sets in \$\mathbb{R}^{\mathbf{n}}\$ by Guy David and Stephen Semmes, they provide several characterizations of uniformly rectifiable sets. In this talk we explore one of the implications included in the monograph, going from an analytic condition to a geometric condition. This talk is purely expository.