Analysis and Mathematical Physics

Several recent groundbreaking results in geometric measure theory, homogeneous dynamics and number theory ultimately rely on a key result of Bourgain known as Bourgain's Projection Theorem (of course, each of these results require many other tools and ideas as well). However, rather than applying Bourgain's Theorem directly, these developments rely on various extensions and generalizations of the Projection Theorem. The goal of the talk is to present an overview of these improvements on Bourgain's Theorem (some of them obtained in collaboration with T. Orponen and H. Wang).