Analysis Learning Seminar

An introduction to the Analyst's Traveling Salesman Theorem with Hölder curves

Lisa Naples (University of Connecticut)

Friday, November 9, 2018 3:30 pm
MONT 414 (Storrs)

In 1990 Peter Jones proved his Analyst's Traveling Salesman Theorem when he provided both necessary and sufficient conditions for a set in $\mathbb{R}^2$ to be contained in the image of a Lipschitz curves.

We will provide a basic introduction to the main techniques used in Jones' work. We will then discuss an extension to Jones' Traveling Salesman Theorem to a wider class of sets. In particular, we will provide 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.