University of Birmingham > Talks@bham > Analysis seminar > Transversality in Harmonic Analysis and the Brascamp–Lieb Inequalities

Transversality in Harmonic Analysis and the Brascamp–Lieb Inequalities

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If you have a question about this talk, please contact Yuzhao Wang.

In modern harmonic analysis, there is a ubiquity of operators whose functional-analytic properties depend on the geometric properties of an underlying submanifold, such as Fourier extension operators and Radon-like transforms. In the analysis of the boundedness of such operators, it is often useful to employ a linear-to-multilinear reduction so that one may appeal to a multilinearised version of the linear estimate one would like to obtain. These multilinear estimates usually require that the submanifolds involved are uniformly transversal in some suitable sense, however, standard linear algebra tools are sometimes insufficient to capture an appropriately general notion of transversality for the estimates in which we are interested. Brascamp–Lieb inequalities offer a robust framework for understanding this higher-order notion transversality in a manner that is well-suited to applications in harmonic analysis and pdes. In my talk, I shall introduce the notion of a Brascamp–Lieb inequality, describe the broader role they play in the subject, and go on to discuss the topic of nonlinear Brascamp–Lieb inequalities, a recent variant that generalises this framework to the manifold setting.

This talk is part of the Analysis seminar series.

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