Seminar | April 10 | 3:30-5 p.m. | 740 Evans Hall
James Rowan, UC Berkeley
The Falconer distance problem asks what the smallest Hausdorff dimension of a compact set E in $R^d$ can be such that its distance set D(E) has positive Lebesgue measure. It is conjectured that if dim E is greater than d/2, then dim D(E) is at least 1. We will discuss the relationship between this problem and spherical averages of Fourier transforms of measures and present a result of Wolff that any set of Hausdorff dimension at least 4/3 in the plane has a distance set of positive Lebesgue measure.