Distance set problem and weighted Fourier extension estimates

Falconer's distance set conjecture states that if a compact subset E of \mathbb{R}^d (d>1) has Hausdorff dimension greater than d/2 then its distance set, D(E):=\{|x-y|:x,y\in E\}, has positive Lebesgue measure.

In this lecture, we will discuss the recent progress in this conjecture and closely related Fourier extension estimates relative to fractal measures.

Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).