学术报告（Jongchon Kim 2026.10.7）

摘要: In this talk, I will present weighted L² Fourier extension estimates for strictly convex C² hypersurfaces with Gaussian curvature comparable to 1, such as the sphere and the truncated paraboloid. As a special case, these estimates recover the fractal L² restriction estimate of Du and Zhang, with sharper dependence on the density of the weight. I will also discuss weighted refined decoupling inequalities for functions satisfying lower-dimensional frequency localization conditions that arise in recent work of Du, Ou, Ren, and Zhang on the Falconer distance set problem.