# Traveling along Hölder curves

I will describe my latest work with L. Naples and V. Vellis, in which we find sufficient conditions to identify (subsets of) Hölder continuous curves of Hausdorff dimension $s>1$. Our conditions are related to the Analyst's Traveling Salesman Theorem, which characterizes subsets of rectifiable curves. On the other hand, standard self-similar sets such as the Sierpinski carpet show that our sufficient condition is not necessary. I will discuss this and other obstructions to the problem of characterizing Hölder curves and their subsets. The core of this talk requires very little background and will be accessible to graduate students, advanced undergraduates, as well as faculty working outside of analysis and geometry.