Speaker: Gareth Speight (University of Cincinnati)

Title: Rademacher’s Theorem and Universal Differentiability Sets

Abstract: Rademacher's theorem states that every Lipschitz function is differentiable almost everywhere. A universal differentiability set (UDS) is a set which contains a point of differentiability for every real-valued Lipschitz function. As a consequence of Rademacher's theorem, every set of positive measure is a UDS. However, many spaces contain a measure zero UDS. This talk will describe what is known in Euclidean spaces, Carnot groups, and Laakso spaces.