UBC Harmonic Analysis and Fractal Geometry: Benjamin Bruce

Given a smooth function Φ:ℝ→ℝd, we ask whether every Borel subset of ℝd with sufficiently high Hausdorff dimension contains a pair of the form {x,x+Φ(t)} with Φ(t)≠0. We prove that a large class of ``curved” functions have this property while certain ``flat” functions do not. This is joint work with Malabika Pramanik.