Dr. Alex McDonald (Dept. of Mathematics, The Ohio State University)

05/01/2023  4:10pm

Abstract: The Falconer distance problem asks how large the Hausdorff dimension of a set must be to ensure it determines a positive Lebesgue measure worth of distances between points.  This is a fundamental problem in the intersection of harmonic analysis and geometric measure theory, and the techniques developed to study it are the jumping off point in the investigation of more complex patterns appearing in fractal sets.  In this talk I will give an introduction to these techniques, and discuss applications to the study of the VC-dimension of naturally arising classes of sets in the fractal setting.