# Lisa Naples

University of Connecticut

**Talk Title:** An Analyst’s Traveling Salesman Theorem for Hölder curves

**Abstract: **In 1990 Peter Jones proved his Analyst’s Traveling Salesman Theorem when he provided both necessary and sufficient conditions for a set in the plane to be contained in the image of a Lipschitz curves. We will provide a brief introduction to the main techniques used in Jones’ work. We will then discuss an extension to Jones’ Traveling Salesman Theorem by providing a sufficient condition for a set to be contained in the image of a (1/s)-Hölder curve for s>1. This talk includes joint work with Matthew Badger and Vyron Vellis.