UBC Harmonic Analysis and Fractal Geometry: Kevin Ren

Given two sets X, Y in R^d, such that X isn't contained in a k-plane, we show that there exists a point x in X such that the radial projection pi_x (Y) has Hausdorff dimension > min(dim(X), dim(Y), k) - eps, for any given eps > 0. This improves a result of Orponen-Shmerkin-Wang by removing a lower bound assumption on dim(Y). The proof borrows heavily from the known d = 2 case, but there are some obstacles. In this talk, we explain the main idea to overcome these obstacles. Then, we will present applications to the Falconer pinned distance set problem in R^d.