UBC Harmonic Analysis and Fractal Geometry: Jacob Fielder

We discuss some recent work on the pinned distance problem in the plane using "effective dimension", a tool from algorithmic information theory. This work improves lower bounds on the dimension of pinned distance sets depending on the Hausdorff and packing dimension of the original set E. In particular, we show that if the packing dimension of E is not much greater than the Hausdorff dimension, then "most" pins give full dimension pinned distance sets. Finally, we consider the problem where the pins are taken to be in a different set than the set the distances are measured to. This is joint work with Don Stull.