| Abstract: |
| Sharp inequalities have a rich tradition in harmonic analysis, going back to the epoch-making works of Beckner and Lieb for the sharp Hausdorff--Young and Hardy--Littlewood--Sobolev inequalities. Even though the history of sharp restriction theory is considerably shorter, it is moving at an incredible pace. In this talk, we survey selected highlights from the past decade, describe some of our own contributions, and pose a few open problems which lie at the interface of euclidean harmonic analysis and dispersive PDE. |
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