Restriction theorems and wave packets

Restriction theorems and wave packets

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John Anderson, Princeton University

 

In this talk, I will describe how wave packets arise naturally in the study of restriction theorems, which concern the behavior of functions whose Fourier transforms are measures on a hypersurface. The goal will be to give an intuitive understanding of how wave packets connect restriction theorems to geometric inequalities of transverse shapes. I will also use induction on scales, a common tool in harmonic analysis, to give a simple proof of such a geometric inequality.