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Abstract

There is a class of problems in harmonic analysis where the curvature of an underlying geometric object plays a central role. For instance, Stein's Fourier restriction conjecture predicts some highly non-trivial estimates for functions whose Fourier transform is supported on a curved manifold such as the sphere. In this talk, I will give a brief survey of this conjecture and discuss related problems about geometric maximal functions. I will explain why polynomial partitioning, a recent technique from discrete geometry, is useful to study these problems.

Registration URL

https://cityu.zoom.us/meeting/register/tJUtcOChqTIpG9ERueUym-gFW1QjwLfETKvv

[Zoom meeting link will be provided via email after registration.]