Falconer's Conjecture

In geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact d-dimensional spaces. We will talk about how the basic Fourier method originated from harmonic analysis could do about the question. Also, we will cover some preliminaries in harmonic analysis and geometric measure theory used in the latter proofs resulting in better estimates.