From Bourgain's Projection Theorem to Kakeya and Khintchine on Fractals: An Impressionistic Picture

This lecture titled "From Bourgain's Projection Theorem to Kakeya and Khintchine on Fractals: An Impressionistic Picture" will be delivered by Pablo Shmerkin from the University of British Columbia as part of the Analysis and Mathematical Physics series at the Institute for Advanced Study on May 13, 2025. Explore how several groundbreaking results in geometric measure theory, homogeneous dynamics, and number theory rely on Bourgain's Projection Theorem, along with various extensions and generalizations of this key result. The talk will present an overview of improvements on Bourgain's Theorem, including work done in collaboration with T. Orponen and H. Wang. The lecture will take place at 2:30pm in Simonyi Hall 101 with remote access options available.