
Title: Analysis on curves in Carnot groups
Abstract: Carnot groups are particularly nice Lie groups, and these manifolds provide mathematical models for scenarios in which motion is controlled by predefined constraints. Such restrictions endow a Carnot group with a non-smooth structure and unusual geometric properties. This unconventional framework requires the development of new and creative solutions to questions of classical analysis. For example, I will illustrate the impact of a Carnot group's metric structure on the smooth extendability of paths, the 1-rectifiability of sets, and the boundedness of singular integral operators defined along curves.