Speaker: Shubham Joshi (University of Hawaii at Mānoa)

Title: Pure Unrectifiability in the Plane

Abstract: A set in the plane is purely unrectifiable if it intersects every rectifiable curve in a set of zero length. This is the antithesis of the notion of a rectifiable set. I will present various results concerning such sets in the plane, with an emphasis on Jordan curves. I will give examples of how one may study this notion for quadratic Julia sets.