Title: Linear patterns in sets
Abstract: Do sets of large Fourier dimension enjoy richer structure than sets of large Hausdorff dimension? Common wisdom and Frostman's lemma would suggest yes; but when it comes to identifying translation-invariant linear patterns in such sets, results often run contrary to intuition. We will review the current literature on linear configurations in large sets and report on ongoing work with Yiyu Liang that attempts to make the above intuition precise.