Gigliola Staffilani: Strichartz Estimates: The dance between analytic number theory and harmonic analysis

In this second lecture I will zoom into the rich mathematics behind the proofs of Strichartz estimates. As mentioned in the first lecture these estimates are fundamental in order to prove well-posedness of dispersive initial value problems by assuming only boundedness of the mass and energy of the initial data. In recent years, while looking for a proof of Strichartz estimates in the periodic setting, a much deeper connection than previously anticipated has been found between analytic number theory and harmonic analysis. I will describe in general terms this connection throughout the lecture.