UBC Harmonic Analysis and Fractal Geometry Seminar: Rosemarie Bongers

Talk Abstract

The orthogonally projected shadows of a dispersed set in the plane carry much of the information about the shape of the set. The average size of the shadow, known as the Favard length, can be used to study density, structure, distribution, rectifiability, and complex analytical properties such as removability. This leads to a rich area of study in geometric measure theory, which ties together ideas from many areas of analysis and probability. In this talk we will discuss how projections can be used to study a set, techniques for estimating Favard length for self-similar sets, and the core properties that make projections useful. This will lead to an idea called transversality and will yield projection theorems for a very general class of projection-type operations, based on joint work with Krystal Taylor (OSU).