Recent progress on distance sets in the plane

Abstract: Recent work has shown that techniques from 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 conjecture. 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, I will discuss recent work which uses algorithmic randomness to improve the best known lower bounds for both the Hausdorff and packing dimensions of pinned distance sets. This is joint work with Jacob Fiedler.

differential geometrylogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic