Colloquium: Projections of random Cantor sets
Speaker: Alan Chang, Washington University in St. Louis
Abstract: The four-corner Cantor set (a.k.a. Garnett set) is a planar analogue of the classical Cantor set and arises in several areas of analysis, including the study of Kakeya sets and removable singularities for analytic functions. A central problem is to understand how this set behaves when projected onto lines. This turns out to be a very difficult question, so we study a random variant of the Cantor set, where we are able to obtain sharp estimates. This is joint work with Pablo Shmerkin and Ville Suomala.