Don Stull : Dimensions of pinned distance sets

Posted by Matthew Harrison-Trainor , part of the Logic Seminar.

At

Oct. 10, 2023, 4 p.m.

In

636 SEO

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.