Logic Seminar
Don Stull
University of Chicago
Dimensions of pinned distance sets
Abstract: Recent work has shown that techniques from computability theory and algorithmic randomness can be used to understand questions in classical geometric measure theory. One of the central problems in geometric measure theory is Falconer's distance set problem. Give a set E in the plane, and a point x, the pinned distance set of E with respect to x is the set of distances between x and the points in E. In this talk, we will discuss ongoing progress on this problem, and present improved lower bounds for both the Hausdorff and packing dimensions of pinned distance sets. We also discuss the computability-theoretic methods used to achieve these bounds.
Tuesday October 10, 2023 at 4:00 PM in 636 SEO