The Brascamp--Lieb inequalities and the restriction problem for the Fourier transform
Seminar Room 1, Newton Institute
The Brascamp--Lieb inequalities simultaneously generalise classical inequalities in analysis such as the multilinear Holder, Young convolution and Loomis--Whitney inequalities. In this talk we will describe certain geometric and combinatorial generalisations of these multilinear inequalities which arise naturally in harmonic analysis and PDE. Particular emphasis will be placed on their intimate connected with the recent restriction theory of the Fourier transform.