UBC Harmonic Analysis and Fractal Geometry: Bobby Wilson

In this talk, we will discuss the classical problem, known as Falconer's distance problem, of quantifying the minimum amount of pairwise distances associated with a given Borel set in Euclidean space. For the last 25 years, methods in harmonic analysis have been the most effective way of approaching this problem. However, we will discuss how certain notions of computational complexity can be used to completely characterize Falconer's distance problem in a class of non-Euclidean Banach spaces.