Explore recent developments in weighted Fourier extension estimates and their applications in partial differential equations and geometric measure theory in this 43-minute lecture. Delve into topics such as the Fourier restriction problem, the relationship between SME and Fourier restriction conjecture, and a generalization of L2 SME. Examine the divergence set of Schrödinger solutions, spherical average Fourier decay rates of fractal measures, and Falconer's distance set problem. Access accompanying presentation slides for a comprehensive understanding of the subject matter.