Some Recent Developments in Harmonic Analysis

I'll explain some work with my collaborators on Sobolev spaces and on Fourier decoupling. It will feature some new ways with which we can compute the L^p norm of the derivative of a function, and some estimates that capture destructive interference between waves that propagate in different directions. Applications will be given in numerical approximations, PDEs, and analytic number theory. Efforts will be made to make this talk accessible to a wide audience.

Joint work with Haim Brezis, Oscar Dominguez, Qingsong Gu, Shaoming Guo, Zane Kun Li, Andreas Seeger, Brian Street, Jean Van Schaftingen, and Pavel Zorin-Kranich.