Szego Seminar: "Fourier Restriction and Geometric Measure Theory"

Abstract: In this talk I will give an overview of the relationship between geometric measure theory and harmonic analysis, and in particular the connection between two open questions: Falconer’s distance set conjecture and the Fourier restriction problem. After defining geometric concepts like Hausdorff dimension and Besicovitch sets, I will introduce Frostman’s lemma as a tool to study these with the language of Fourier transforms. Finally, I will mention important results like the Wolff-Erdoğan and Stein-Thomas theorems, as well as Tao’s bilinear restriction estimate.

Host: Nathan Wagner